#include using namespace std; using int64 = long long; // const int mod = 1e9 + 7; const int mod = 31607; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } 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< int > &ofs, vector< Edge > &edges, vector< tcap_t > &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< int > 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< cap_t >(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< int > &ofs; vector< Edge > &edges; vector< tcap_t > &capacity; vector< int > 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< bool, tcost_t > 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< cost_t >(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< tcap_t > excess(initial_excess); for(auto &e : edges) excess[e.to] -= e.cap; vector< int > 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< tcost_t >(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< tcap_t >(excess[u], residue(e)); push(u, e, df); if(!excess[u]) return; } else delta = min< tcost_t >(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< InputEdge > in; vector< tcap_t > capacity; vector< int > ofs; vector< Edge > edges; tcost_t initial_cost; vector< tcap_t > initial_excess; vector< tcost_t > potential; }; // cap, total_cap, cost * (2 * |V|), total_cost using MCC = CostScaling< int64_t, int64_t, int64_t, int64_t >; int main() { int N, M, K, L; cin >> N >> M >> K >> L; MCC flow(N + M + 2, L + N + 2); int S = N + M, T = N + M + 1; for(int i = 0; i < L; i++) { int x, y, z; cin >> x >> y >> z; --x, --y; flow.add_directed_edge(x, y + N, 0, 1, -(1 << z)); } for(int i = 0; i < N; i++) { flow.add_directed_edge(S, i, 0, 1, 0); flow.add_directed_edge(i, T, 0, 1, 0); } for(int i = 0; i < M; i++) { flow.add_directed_edge(i + N, T, 0, 1, 0); } flow.add_directed_edge(T, S, N, N, 0); cout << -flow.minimum_cost_circulation().second << "\n"; }