#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif #include // Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed) // Verified: // - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702 // - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT template ::max() / 2> struct MinCostFlow { template struct csr { std::vector start; std::vector elist; explicit csr(int n, const std::vector> &edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) { start[e.first + 1]++; } for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; } auto counter = start; for (auto e : edges) { elist[counter[e.first]++] = e.second; } } }; public: MinCostFlow() {} explicit MinCostFlow(int n) : is_dual_infeasible(false), _n(n) { static_assert(std::numeric_limits::max() > 0, "max() must be greater than 0"); } int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); if (cost < 0) is_dual_infeasible = true; int m = int(_edges.size()); _edges.push_back({from, to, cap, 0, cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(_edges.size()); assert(0 <= i && i < m); return _edges[i]; } std::vector edges() { return _edges; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); int m = int(_edges.size()); std::vector edge_idx(m); auto g = [&]() { std::vector degree(_n), redge_idx(m); std::vector> elist; elist.reserve(2 * m); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] = degree[e.from]++; redge_idx[i] = degree[e.to]++; elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}}); elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}}); } auto _g = csr<_edge>(_n, elist); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] += _g.start[e.from]; redge_idx[i] += _g.start[e.to]; _g.elist[edge_idx[i]].rev = redge_idx[i]; _g.elist[redge_idx[i]].rev = edge_idx[i]; } return _g; }(); auto result = slope(g, s, t, flow_limit); for (int i = 0; i < m; i++) { auto e = g.elist[edge_idx[i]]; _edges[i].flow = _edges[i].cap - e.cap; } return result; } private: bool is_dual_infeasible; int _n; std::vector _edges; // inside edge struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> slope(csr<_edge> &g, int s, int t, Cap flow_limit) { // variants (C = maxcost): // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0 // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge // dual_dist[i] = (dual[i], dist[i]) std::vector> dual_dist(_n); if (is_dual_infeasible) { auto check_dag = [&]() { std::vector deg_in(_n); for (int v = 0; v < _n; v++) { for (int i = g.start[v]; i < g.start[v + 1]; i++) { deg_in[g.elist[i].to] += g.elist[i].cap > 0; } } std::vector st; st.reserve(_n); for (int i = 0; i < _n; i++) { if (!deg_in[i]) st.push_back(i); } for (int n = 0; n < _n; n++) { if (int(st.size()) == n) return false; // Not DAG int now = st[n]; for (int i = g.start[now]; i < g.start[now + 1]; i++) { const auto &e = g.elist[i]; if (!e.cap) continue; deg_in[e.to]--; if (deg_in[e.to] == 0) st.push_back(e.to); if (dual_dist[e.to].first >= dual_dist[now].first + e.cost) dual_dist[e.to].first = dual_dist[now].first + e.cost; } } return true; }(); if (!check_dag) throw; auto dt = dual_dist[t].first; for (int v = 0; v < _n; v++) dual_dist[v].first -= dt; is_dual_infeasible = false; } std::vector prev_e(_n); std::vector vis(_n); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::vector que_min; std::vector que; auto dual_ref = [&]() { for (int i = 0; i < _n; i++) { dual_dist[i].second = std::numeric_limits::max(); } std::fill(vis.begin(), vis.end(), false); que_min.clear(); que.clear(); // que[0..heap_r) was heapified unsigned heap_r = 0; dual_dist[s].second = 0; que_min.push_back(s); while (!que_min.empty() || !que.empty()) { int v; if (!que_min.empty()) { v = que_min.back(); que_min.pop_back(); } else { while (heap_r < que.size()) { heap_r++; std::push_heap(que.begin(), que.begin() + heap_r); } v = que.front().to; std::pop_heap(que.begin(), que.end()); que.pop_back(); heap_r--; } if (vis[v]) continue; vis[v] = true; if (v == t) break; // dist[v] = shortest(s, v) + dual[s] - dual[v] // dist[v] >= 0 (all reduced cost are positive) // dist[v] <= (n-1)C Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second; for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto e = g.elist[i]; if (!e.cap) continue; // |-dual[e.to] + dual[v]| <= (n-1)C // cost <= C - -(n-1)C + 0 = nC Cost cost = e.cost - dual_dist[e.to].first + dual_v; if (dual_dist[e.to].second - dist_v > cost) { Cost dist_to = dist_v + cost; dual_dist[e.to].second = dist_to; prev_e[e.to] = e.rev; if (dist_to == dist_v) { que_min.push_back(e.to); } else { que.push_back(Q{dist_to, e.to}); } } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; // dual[v] = dual[v] - dist[t] + dist[v] // = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + // (shortest(s, v) + dual[s] - dual[v]) = - shortest(s, // t) + dual[t] + shortest(s, v) = shortest(s, v) - // shortest(s, t) >= 0 - (n-1)C dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost_per_flow = -1; std::vector> result = {{Cap(0), Cost(0)}}; while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = g.elist[prev_e[v]].to) { c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap); } for (int v = t; v != s; v = g.elist[prev_e[v]].to) { auto &e = g.elist[prev_e[v]]; e.cap += c; g.elist[e.rev].cap -= c; } Cost d = -dual_dist[s].first; flow += c; cost += c * d; if (prev_cost_per_flow == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost_per_flow = d; } return result; } }; int main() { auto sort_by_subtree_size = [&](const vector> &to, vector &st, bool add_all = false) { const int N = to.size(); vector> stuv; for (auto [root, par] : st) { int cnt = 0; auto rec = [&](auto &&self, int now, int prv) -> void { cnt++; for (auto nxt : to[now]) { if (nxt == prv) continue; self(self, nxt, now); } }; rec(rec, root, par); stuv.emplace_back(cnt, root, par); } sort(stuv.begin(), stuv.end()); st.clear(); for (auto [s, u, v] : stuv) st.emplace_back(u, v); REP(i, N) { st.emplace_back(i, -1), stuv.emplace_back(N, i, -1); if (!add_all) break; } return stuv; }; int K; cin >> K; vector> to1(K); vector st1; REP(i, K - 1) { int a, b; cin >> a >> b; --a, --b; REP(t, 2) { to1[a].push_back(b); st1.emplace_back(a, b); swap(a, b); } } auto size_uv_1 = sort_by_subtree_size(to1, st1, true); map finder1; REP(i, st1.size()) finder1[st1[i]] = i; int N; cin >> N; vector> to2(N); vector st2; REP(i, N - 1) { int a, b; cin >> a >> b; --a, --b; REP(t, 2) { to2[a].emplace_back(b); st2.emplace_back(a, b); swap(a, b); } } auto size_uv_2 = sort_by_subtree_size(to2, st2); map finder2; REP(i, st2.size()) finder2[st2[i]] = i; const int size_diff = N - K; vector dp(st2.size(), vector(st1.size(), -1000000)); int ans = 0; REP(t2, st2.size()) { auto [root2, par2] = st2[t2]; vector ind2; for (auto ch2 : to2[root2]) { if (ch2 == par2) continue; int nx2 = finder2.at(pint(ch2, root2)); REP(j, dp[t2].size()) { chmax(dp[t2][j], dp[nx2][j] + 1); } ind2.push_back(nx2); } REP(t1, st1.size()) { const int sz1 = get<0>(size_uv_1[t1]), sz2 = get<0>(size_uv_2[t2]); if (sz1 > sz2) continue; if (sz1 + (N - sz2) < K) continue; const auto [root1, par1] = st1[t1]; vector ind1; for (auto ch1 : to1[root1]) { if (ch1 == par1) continue; int nx1 = finder1.at(make_pair(ch1, root1)); ind1.push_back(nx1); } int L1 = ind1.size(), R2 = ind2.size(); const int gs = L1 + R2, gt = gs + 1; MinCostFlow graph(gt + 1); // graph.set_supply(gs, L1); // graph.set_supply(gt, -L1); // REP(i, L1) graph.add_edge(gs, i, 0, 1, 0); REP(i, L1) graph.add_edge(gs, i, 1, 0); // REP(i, R2) graph.add_edge(L1 + i, gt, 0, 1, 0); REP(i, R2) graph.add_edge(L1 + i, gt, 1, 0); REP(i, L1) REP(j, R2) { int k2 = ind2[j]; int k1 = ind1[i]; // if (dp[k2][k1] > 0) graph.add_edge(i, L1 + j, 0, 1, -dp[k2][k1]); if (dp[k2][k1] > 0) graph.add_edge(i, L1 + j, 1, -dp[k2][k1]); } auto ret = graph.flow(gs, gt); // auto ret = graph.solve(); // if (!graph.infeasible or L1 == 0) { // chmax(dp[t2][t1], -ret + 1); // if (sz1 == K) chmax(ans, -ret + 1); // } if (ret.first == L1) { chmax(dp[t2][t1], -ret.second + 1); if (sz1 == K) chmax(ans, -ret.second + 1); } } } cout << ans - 1 << '\n'; }