#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, pair& p){return is >> p.first >> p.second;} template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const pair& p){return os << p.first << " " << p.second;} template ostream& operator << (ostream& os, const vector& vec){for(size_t i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(size_t i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; // min cost flow // https://min-25.hatenablog.com/entry/2017/09/08/182320 template < typename CapType, typename TotalCapType, typename CostType, typename TotalCostType > class CostScaling { private: static const int alpha = 8; // eps <- max(1, eps / alpha) using cap_t = CapType; using tcap_t = TotalCapType; using cost_t = CostType; // > max{|C|} * (2 * |V|) using tcost_t = TotalCostType; static constexpr cost_t Inf = (tcap_t(1) << (sizeof(tcap_t) * 8 - 2)) - 1; struct InputEdge { int from, to; cap_t b, c; cost_t cost; }; struct Edge { int to, rev; cap_t cap; cost_t cost; }; class Dinic { public: Dinic(int N, const vector& ofs, vector& edges, vector& capacity) : N(N), ofs(ofs), edges(edges), capacity(capacity), last(N) {} bool succeeded() { // s -> u: capacity[u] // u -> t: capacity[u + N] tcap_t f = 0; for (int u = 0; u < N; ++u) f += capacity[u]; vector que(N); while (f) { dist.assign(N, -1); int qh = 0, qt = 0, lv = N; for (int u = 0; u < N; ++u) if (capacity[u] > 0) que[qt++] = u, dist[u] = 0; for (; qh < qt; ) { int u = que[qh++]; if (lv == N && capacity[u + N] > 0) lv = dist[u]; if (dist[u] > lv) break; for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) { int v = edges[ei].to; if (edges[ei].cap > 0 && dist[v] == -1) { que[qt++] = v, dist[v] = dist[u] + 1; } } } if (lv == N) break; for (int u = 0; u < N; ++u) last[u] = ofs[u]; for (int u = 0; u < N; ++u) if (capacity[u] > 0) { auto df = block_flow(u, capacity[u]); f -= df, capacity[u] -= df; } } return f == 0; } private: tcap_t block_flow(int u, tcap_t f) { tcap_t ret = 0; if (capacity[u + N] > 0) { tcap_t df = min(f, capacity[u + N]); capacity[u + N] -= df; return df; } for (auto& ei = last[u]; ei < ofs[u + 1]; ++ei) { auto& e = edges[ei]; int v = e.to; if (e.cap == 0 || dist[v] <= dist[u]) continue; cap_t df = block_flow(v, min(e.cap, f)); if (df == 0) continue; e.cap -= df, edges[e.rev].cap += df; f -= df, ret += df; if (f == 0) break; } return ret; } int N; const vector& ofs; vector& edges; vector& capacity; vector last, dist; }; public: CostScaling(int N, int M=0) : N(N), capacity(2 * N) { if (M > 0) in.reserve(M); } void add_directed_edge(int u, int v, cap_t b, cap_t c, cost_t cost) { if (b > 0) capacity[v] += b, capacity[u + N] += b; else capacity[u] += -b, capacity[v + N] += -b; in.push_back({u, v, b, c, cost}); } pair minimum_cost_circulation() { construct(); if (!has_feasible_circulation()) return {false, 0}; const int cost_multiplier = 2 << __lg(N); // should be > |V| cost_t eps = 0; for (auto& e : edges) e.cost *= cost_multiplier, eps = max(eps, e.cost); while (eps > 1) refine(eps = max(1, eps / alpha)); tcost_t ret = initial_cost; for (auto& e : edges) ret -= (e.cost / cost_multiplier) * e.cap; return {true, ret / 2}; } private: void refine(const cost_t eps) { auto cost_p = [&] (int u, const Edge& e) { return e.cost + potential[u] - potential[e.to]; }; for (int u = 0; u < N; ++u) for (int i = ofs[u]; i < ofs[u + 1]; ++i) { auto& e = edges[i]; if (cost_p(u, e) < 0) edges[e.rev].cap += e.cap, e.cap = 0; } vector excess(initial_excess); for (auto& e : edges) excess[e.to] -= e.cap; vector stack; stack.reserve(N); for (int u = 0; u < N; ++u) if (excess[u] > 0) stack.push_back(u); auto residue = [&] (const Edge& e) -> cap_t { return e.cap; }; auto push = [&] (int u, Edge& e, cap_t df) { e.cap -= df; edges[e.rev].cap += df; excess[e.to] += df; excess[u] -= df; if (excess[e.to] > 0 && excess[e.to] <= df) { stack.push_back(e.to); } }; auto relabel = [&] (int u, cost_t delta) { potential[u] -= delta + eps; }; auto relabel_in_advance = [&] (int u) { if (excess[u] != 0) return false; auto delta = Inf; for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) { auto& e = edges[ei]; if (residue(e) == 0) continue; if (cost_p(u, e) < 0) return false; else delta = min(delta, cost_p(u, e)); } relabel(u, delta); return true; }; auto discharge = [&] (int u) { auto delta = Inf; for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) { auto& e = edges[ei]; if (residue(e) == 0) continue; if (cost_p(u, e) < 0) { if (relabel_in_advance(e.to)) { --ei; continue; // modify ei (!) } cap_t df = min(excess[u], residue(e)); push(u, e, df); if (!excess[u]) return; } else delta = min(delta, cost_p(u, e)); } relabel(u, delta); stack.push_back(u); }; while (!stack.empty()) { auto u = stack.back(); stack.pop_back(); discharge(u); } } void construct() { ofs.assign(N + 1, 0); edges.resize(2 * in.size()); initial_excess.assign(N, 0); initial_cost = 0; potential.assign(N, 0); for (auto& e : in) ofs[e.from + 1]++, ofs[e.to + 1]++; for (int i = 1; i <= N; ++i) ofs[i] += ofs[i - 1]; for (auto& e : in) { initial_excess[e.to] += e.c; initial_excess[e.from] += -e.b; initial_cost += tcost_t(e.cost) * (e.c + e.b); edges[ofs[e.from]++] = {e.to, ofs[e.to], e.c - e.b, e.cost}; edges[ofs[e.to]++] = {e.from, ofs[e.from] - 1, 0, -e.cost}; } for (int i = N; i > 0; --i) ofs[i] = ofs[i - 1]; ofs[0] = 0; } bool has_feasible_circulation() { return Dinic(N, ofs, edges, capacity).succeeded(); } private: int N; vector in; vector capacity; vector ofs; vector edges; tcost_t initial_cost; vector initial_excess; vector potential; }; // cap, total_cap, cost * (2 * |V|), total_cost using MCC = CostScaling; // using MCC = CostScaling; int main(){ int n; cin >> n; vector> v(n); cin >> v; // Min_Cost_Flow f(n + n + 1 + 2, 1000000000); MCC f(n+n+3); int source = n+n+1; int sink = source+1; int odd = n+n; // f.add_edge(odd, sink, n/3, 0); f.add_directed_edge(odd, sink, n/3, n/3, 0); for(int i=0; i