#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() #define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin()) #define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin()) using ll=long long int; using ull=unsigned long long; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} templateT ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);} templateT floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);} templateint popcnt(T x){return __builtin_popcountll(x);} templateint topbit(T x){return (x==0?-1:63-__builtin_clzll(x));} templateint lowbit(T x){return (x==0?-1:__builtin_ctzll(x));} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__int128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__uint128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(double x){ ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); _write(s); } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ _write(head); write(tail...); if(space)_write(' '); } inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Graph/maxflow.hpp" struct MaxFlow { struct Edge { int to, rev; ll cap; }; int V; vector> G; vector itr, level; using P = pair; vector

es; public: MaxFlow() {} MaxFlow(int V) : V(V) { G.assign(V, vector()); } int add_vertex() { G.push_back(vector()); return V++; } void add_edge(int from, int to, ll cap) { es.push_back({from, (int)G[from].size()}); G[from].push_back({to, (int)G[to].size(), cap}); G[to].push_back({from, (int)G[from].size() - 1, 0}); } struct Type { int from, to; ll cap, recap; }; Type get_edge(int i) { auto [from, pos] = es[i]; auto e = G[from][pos]; auto re = G[e.to][e.rev]; return Type{from, e.to, e.cap, re.cap}; } void bfs(int s) { level.assign(V, -1); queue q; level[s] = 0; q.push(s); while (!q.empty()) { int v = q.front(); q.pop(); for (auto &e : G[v]) { if (e.cap > 0 && level[e.to] < 0) { level[e.to] = level[v] + 1; q.push(e.to); } } } } ll dfs(int v, int t, ll f) { if (v == t) return f; for (int &i = itr[v]; i < (int)G[v].size(); i++) { Edge &e = G[v][i]; if (e.cap > 0 && level[v] < level[e.to]) { ll d = dfs(e.to, t, min(f, e.cap)); if (d > 0) { e.cap -= d, G[e.to][e.rev].cap += d; return d; } } } return 0; } ll run(int s, int t) { ll ret = 0, f; while (bfs(s), level[t] >= 0) { itr.assign(V, 0); while ((f = dfs(s, t, INF)) > 0) ret += f; } return ret; } }; /** * @brief Maximum Flow */ #line 5 "sol.cpp" // yosupo orz template struct MinCostFlow { struct X { int from, to; Cap lb, ub, flow; Cost cost; }; struct Edge { int to, rev; Cap cap; Cost cost; }; using P = pair; int n, m; vector es; vector exc; vector dual; vector> g; Cost MX; MinCostFlow(int _n) : n(_n), m(0), exc(n), dual(n), g(n), MX(0) {} void add_edge(int from, int to, Cap lb, Cap ub, Cost cost) { m++; chmax(MX, cost); chmax(MX, -cost); es.push_back({from, to, lb, ub, 0, cost}); } void add_excess(int v, Cap c) { exc[v] += c; } pair run() { MaxFlow mf(n + 2); int S = n, T = n + 1; Cap psum = 0, nsum = 0; rep(i, 0, n) { if (exc[i] > 0) { psum += exc[i]; mf.add_edge(S, i, exc[i]); } if (exc[i] < 0) { nsum += -exc[i]; mf.add_edge(i, T, -exc[i]); } } for (auto &e : es) { exc[e.to] += e.lb; exc[e.from] -= e.lb; mf.add_edge(e.from, e.to, e.ub - e.lb); } if (psum != nsum or mf.run(S, T) != psum) return {false, 0}; using P = pair; vector

pos; rep(i, 0, m) { auto e = mf.get_edge(i); Cost cost = es[i].cost * n; int fid = SZ(g[e.from]), tid = SZ(g[e.to]); if (e.from == e.to) tid++; pos.push_back({e.from, fid}); g[e.from].push_back({e.to, tid, e.cap, cost}); g[e.to].push_back({e.from, fid, e.recap, -cost}); } // solve Cost eps = MX * n + 1; while (eps > 1) { eps = max(eps >> 2, 1); refine(eps); } Cost ret = 0; rep(i, 0, m) { auto [from, fid] = pos[i]; es[i].flow = es[i].ub - g[from][fid].cap; ret += es[i].flow * es[i].cost; } for (;;) { bool upd = 0; rep(i, 0, n) { for (auto &e : g[i]) if (e.cap) { auto cost = dual[i] + e.cost / n; if (chmin(dual[e.to], cost)) { upd = 1; } } } if (!upd) break; } return {true, ret}; } private: void refine(Cost &eps) { vector used(n); queue que; vector iter(n); auto cost = [&](int from, const Edge &e) { return e.cost + dual[from] - dual[e.to]; }; auto push = [&](int from, Edge &e, Cap cap) { exc[from] -= cap; exc[e.to] += cap; g[e.to][e.rev].cap += cap; e.cap -= cap; }; auto relabel = [&](int v) { iter[v] = 0; Cost down = MX * (n + 1); for (auto &e : g[v]) if (e.cap) { chmin(down, eps + cost(v, e)); } dual[v] -= down; que.push(v); used[v] = 1; }; rep(i, 0, n) { for (auto &e : g[i]) if (e.cap and cost(i, e) < 0) { push(i, e, e.cap); } } rep(i, 0, n) if (exc[i] > 0) { used[i] = 1; que.push(i); } while (!que.empty()) { auto v = que.front(); que.pop(); used[v] = 0; for (int &i = iter[v]; i < SZ(g[v]); i++) { auto &e = g[v][i]; if (e.cap and cost(v, e) < 0) { push(v, e, min(exc[v], e.cap)); if (!used[e.to] and exc[e.to] > 0) { used[e.to] = 1; que.push(e.to); } if (exc[v] == 0) break; } } if (exc[v] > 0) relabel(v); } eps = 0; rep(i, 0, n) { for (auto &e : g[i]) if (e.cap) { chmax(eps, -cost(i, e)); } } } }; FastIO io; int main() { int n, m, k, L; io.read(n, m, k, L); vector x(L), y(L), z(L); rep(i, 0, L) { io.read(x[i], y[i], z[i]); } MinCostFlow buf(n + m + 1); int S = n + m; rep(i, 0, n) { buf.add_edge(S, i, 0, 1, 0); } rep(i, 0, m) { buf.add_edge(n + i, S, 0, 1, 0); } rep(i, 0, L) { buf.add_edge(x[i] - 1, y[i] - 1 + n, 0, 1, -(1 << z[i])); } auto [_, ret] = buf.run(); io.write(-ret); return 0; }