/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; // 前方宣言 template istream &operator>>(istream &is, vc &vec); template ostream &operator<<(ostream &os, const vc &vec); template ostream &operator>>(ostream &os, const vc &vec); template istream &operator>>(istream &is, array &arr); template ostream &operator<<(ostream &os, const array &arr); template ostream &operator>>(ostream &os, const array &arr); template istream &operator>>(istream &is, pair &pair_var); template ostream &operator<<(ostream &os, const pair &pair_var); template ostream &out_iter(ostream &os, const T &map_var); template ostream &operator<<(ostream &os, const map &map_var); template ostream &operator<<(ostream &os, const um &map_var); template ostream &operator<<(ostream &os, const set &set_var); template ostream &operator<<(ostream &os, const us &set_var); template ostream &operator<<(ostream &os, const pq &pq_var); template ostream &operator<<(ostream &os, const queue &queue_var); template ostream &operator<<(ostream &os, const stack &stk_var); template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<< (os, a); } return os; } template void print_tuple(tuple &a) { operator<< <0, true>(std::cout, a); } void pprint() { std::cout << endl; } template void pprint(Head &&head, Tail &&...tail) { std::cout << head; if (sizeof...(Tail) > 0) std::cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((std::cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr); std::cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) std::cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; /* #region Graph */ // エッジ(本来エッジは双方向だが,ここでは単方向で管理) template struct Edge { int src; // エッジ始点となる頂点 int dst; // エッジ終点となる頂点 weight_t weight; // 重み flow_t cap; Edge() : src(0), dst(0), weight(0) {} Edge(int src, int dst, weight_t weight) : src(src), dst(dst), weight(weight) {} Edge(int src, int dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {} // Edge 標準出力 friend ostream &operator<<(ostream &os, Edge &edge) { os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")"; return os; } }; // 同じ頂点を始点とするエッジ集合 template class Node : public vc> { public: int idx; Node() : vc>() {} // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); }; }; // graph[i] := 頂点 i を始点とするエッジ集合 template class Graph : public vc> { public: Graph() : vc>() {} Graph(int n) : vc>(n) { REP(i, 0, n)(*this)[i].idx = i; } /** 単方向 */ void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); } /** 双方向 */ void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); } /** ノード追加 */ int add_node() { int idx = (int)this->size(); this->emplace_back(); Node &node = this->back(); node.idx = idx; return idx; } }; // using Array = vc; // using Matrix = vc; /* #endregion */ /* #region scc */ // 強連結成分分解 template pair> scc(const Graph &g) { ll n = SIZE(g); // ノード数 Graph rg(n); // 逆向きのグラフ for (const Node &es : g) { for (Edge e : es) { // e はエッジのコピー swap(e.src, e.dst); rg[e.src].emplace_back(e); } } vc order; order.reserve(n); { // dfs 1回目 vc visited(n), added(n); REP(i, 0, n) { if (visited[i]) continue; stack stk; stk.push(i); while (!stk.empty()) { int cur = stk.top(); visited[cur] = true; bool pushed = false; for (const Edge &e : g[cur]) if (!visited[e.dst]) stk.push(e.dst), pushed = true; if (!pushed) { // カレントノードからは未訪問ノードへ到達できない int t = stk.top(); stk.pop(); // 未訪問ノードへ到達できないノードは除いていく if (!added[t]) added[t] = true, order.push_back(t); } } } reverse(ALL(order)); } vc group_indices(n, -1); int groupnum = 0; { // dfs 2回目 for (int &v : order) { if (group_indices[v] != -1) continue; stack stk; stk.push(v); while (!stk.empty()) { int cur = stk.top(); stk.pop(), group_indices[cur] = groupnum; for (Edge &e : rg[cur]) if (group_indices[e.dst] == -1) stk.push(e.dst); } ++groupnum; } } return {groupnum, group_indices}; } /* #endregion */ // Problem void solve() { VAR(ll, n); vll m(n); vvll a(n); REP(i, 0, n) { cin >> m[i]; a[i].resize(m[i]); cin >> a[i]; a[i]--; } Graph<> graph(n); REP(i, 0, n) REP(j, 0, m[i]) graph.add_arc(i, a[i][j]); const auto [groupnum, group_indices] = scc(graph); // dump(groupnum, group_indices); if (groupnum == 1) { Yn(true); return; } // DAG を作ったときに,行き止まりノード(出次数が0)のノードが2つ以上あったらNG vvll dag_edges(groupnum); REP(i, 0, n) REP(j, 0, m[i]) { const ll src = group_indices[i]; const ll dst = group_indices[a[i][j]]; if (src == dst) continue; dag_edges[src].push_back(dst); } vll in_deg(groupnum, 0); vll out_deg(groupnum, 0); REP(i, 0, groupnum) { sort(ALL(dag_edges[i])); UNIQ(dag_edges[i]); for (const ll &dst : dag_edges[i]) { // dag.add_arc(i, dst); out_deg[i]++; in_deg[dst]++; } } // dump(out_deg); ll zero = 0; for (const ll ° : out_deg) { if (deg == 0) zero++; } if (zero >= 2) { Yn(false); return; } // 人1 のグループは出次数が正である必要がある if (out_deg[group_indices[0]] == 0) { Yn(false); return; } // 人1 のグループ以外に,入次数が 0 のグループがあったらNG // 人1 のグループは入次数が 0 でないといけない(1以上の場合,そっちに行けないので) REP(gi, 0, groupnum) { if (gi == group_indices[0]) { if (in_deg[gi] > 0) { Yn(false); return; } } else { if (in_deg[gi] == 0) { Yn(false); return; } } } // ★DAGを作ったときに,枝分かれして合流するような形は NG // 出次数2以上のノードがあったときに,そのノードまで消費したときに // 入次数が 0 になってしまうノードが2つ以上あったら NG vll in_deg_cp = in_deg; // dump(group_indices, in_deg_cp); Graph<> dag(groupnum); REP(i, 0, groupnum) { sort(ALL(dag_edges[i])); UNIQ(dag_edges[i]); for (const ll &dst : dag_edges[i]) { dag.add_arc(i, dst); } } queue que; que.push(group_indices[0]); while (SIZE(que)) { const ll cur = que.front(); que.pop(); // cur から遷移できる先の入次数を減じる for (const Edge<> &edge : dag[cur]) { if (--in_deg_cp[edge.dst] == 0) { que.push(edge.dst); } } if (SIZE(que) >= 2) { Yn(false); return; } } // 入次数をすべて消費していればOK // dump(__LINE__); // dump(in_deg_cp); Yn(accumulate(ALL(in_deg_cp), 0LL) == 0LL); } // entry point int main() { solve(); return 0; }