#include using namespace std; // https://judge.yosupo.jp/submission/51957 struct linked_lists { int L, N; vector next, prev; // L: lists are [0...L), N: integers are [0...N) explicit linked_lists(int L = 0, int N = 0) { assign(L, N); } int rep(int l) const { return l + N; } int head(int l) const { return next[rep(l)]; } int tail(int l) const { return prev[rep(l)]; } bool empty(int l) const { return next[rep(l)] == rep(l); } void init(int l, int n) { meet(rep(l), n, rep(l)); } void clear(int l) { next[rep(l)] = prev[rep(l)] = rep(l); } void push_front(int l, int n) { assert(l < L && n < N), meet(rep(l), n, head(l)); } void push_back(int l, int n) { assert(l < L && n < N), meet(tail(l), n, rep(l)); } void insert_before(int i, int n) { assert(i < N && n < N), meet(prev[i], n, i); } void insert_after(int i, int n) { assert(i < N && n < N), meet(i, n, next[i]); } void erase(int n) { assert(n < N), meet(prev[n], next[n]); } void pop_front(int l) { assert(l < L && !empty(l)), meet(rep(l), next[head(l)]); } void pop_back(int l) { assert(l < L && !empty(l)), meet(prev[tail(l)], rep(l)); } void splice_front(int l, int b) { if (l != b && !empty(b)) meet(tail(b), head(l)), meet(rep(l), head(b)), clear(b); } void splice_back(int l, int b) { if (l != b && !empty(b)) meet(tail(l), head(b)), meet(tail(b), rep(l)), clear(b); } void clear() { iota(begin(next) + N, end(next), N); iota(begin(prev) + N, end(prev), N); } void assign(int L, int N) { this->L = L, this->N = N; next.resize(N + L), prev.resize(N + L), clear(); } private: inline void meet(int u, int v) { next[u] = v, prev[v] = u; } inline void meet(int u, int v, int w) { meet(u, v), meet(v, w); } }; #define FOR_EACH_IN_LINKED_LIST(i, l, lists) \ for (int z##i = l, i = lists.head(z##i); i != lists.rep(z##i); i = lists.next[i]) #define FOR_EACH_IN_LINKED_LIST_REVERSE(i, l, lists) \ for (int z##i = l, i = lists.tail(z##i); i != lists.rep(z##i); i = lists.prev[i]) template struct network_simplex { explicit network_simplex(int V) : V(V), node(V + 1) {} void add(int u, int v, Flow lower, Flow upper, Cost cost) { assert(0 <= u && u < V && 0 <= v && v < V); edge.push_back({{u, v}, lower, upper, cost}), E++; } void add_supply(int u, Flow supply) { node[u].supply += supply; } void add_demand(int u, Flow demand) { node[u].supply -= demand; } auto get_supply(int u) const { return node[u].supply; } auto get_potential(int u) const { return node[u].pi; } auto get_flow(int e) const { return edge[e].flow; } auto get_circulation_cost() const { CostSum sum = 0; for (int e = 0; e < E; e++) { sum += edge[e].flow * CostSum(edge[e].cost); } return sum; } auto mincost_circulation() { static constexpr bool INFEASIBLE = false, OPTIMAL = true; Flow sum_supply = 0; for (int u = 0; u < V; u++) { sum_supply += node[u].supply; } if (sum_supply != 0) { return INFEASIBLE; } for (int e = 0; e < E; e++) { if (edge[e].lower > edge[e].upper) { return INFEASIBLE; } } init(); int in_arc = select_pivot_edge(); while (in_arc != -1) { pivot(in_arc); in_arc = select_pivot_edge(); } for (int e = 0; e < E; e++) { auto [u, v] = edge[e].node; edge[e].flow += edge[e].lower; edge[e].upper += edge[e].lower; node[u].supply += edge[e].lower; node[v].supply -= edge[e].lower; } for (int e = E; e < E + V; e++) { if (edge[e].flow != 0) { edge.resize(E); return INFEASIBLE; } } edge.resize(E); return OPTIMAL; } private: enum ArcState : int8_t { STATE_UPPER = -1, STATE_TREE = 0, STATE_LOWER = 1 }; struct Node { int parent, pred; Flow supply; CostSum pi; }; struct Edge { int node[2]; Flow lower, upper; Cost cost; Flow flow = 0; ArcState state = STATE_LOWER; }; int V, E = 0, next_arc = 0, block_size = 0; vector node; vector edge; linked_lists children; vector bfs; // scratchpad for pi bfs and upwards walk auto reduced_cost(int e) const { auto [u, v] = edge[e].node; return edge[e].cost + node[u].pi - node[v].pi; } void init() { Cost slack_cost = 0; for (int e = 0; e < E; e++) { auto [u, v] = edge[e].node; edge[e].flow = 0; edge[e].state = STATE_LOWER; edge[e].upper -= edge[e].lower; node[u].supply -= edge[e].lower; node[v].supply += edge[e].lower; slack_cost += edge[e].cost < 0 ? -edge[e].cost : edge[e].cost; } edge.resize(E + V); bfs.resize(V + 1); children.assign(V + 1, V + 1); next_arc = 0; // Remove non-zero lower bounds int root = V; node[root] = {-1, -1, 0, 0}; for (int u = 0, e = E; u < V; u++, e++) { node[u].parent = root, node[u].pred = e; children.push_back(root, u); auto supply = node[u].supply; if (supply >= 0) { node[u].pi = -slack_cost; edge[e] = {{u, root}, 0, supply, slack_cost, supply, STATE_TREE}; } else { node[u].pi = slack_cost; edge[e] = {{root, u}, 0, -supply, slack_cost, -supply, STATE_TREE}; } } block_size = max(int(ceil(sqrt(V + 1))), min(10, V + 1)); } int select_pivot_edge() { // lemon-like block search int in_arc = -1; int count = block_size, seen_edges = E + V; Cost minimum = 0; for (int e = next_arc; seen_edges-- > 0; e = e + 1 == E + V ? 0 : e + 1) { if (minimum > edge[e].state * reduced_cost(e)) { minimum = edge[e].state * reduced_cost(e); in_arc = e; } if (--count == 0 && minimum < 0) { next_arc = e + 1 == E + V ? 0 : e + 1; return in_arc; } else if (count == 0) { count = block_size; } } return in_arc; } void pivot(int in_arc) { // Find join node auto [u_in, v_in] = edge[in_arc].node; int a = u_in, b = v_in; while (a != b) { a = node[a].parent == -1 ? v_in : node[a].parent; b = node[b].parent == -1 ? u_in : node[b].parent; } int join = a; // we add flow to source->target int source = edge[in_arc].state == STATE_LOWER ? u_in : v_in; int target = edge[in_arc].state == STATE_LOWER ? v_in : u_in; enum OutArcSide { SAME_EDGE, FIRST_SIDE, SECOND_SIDE }; Flow flow_delta = edge[in_arc].upper; OutArcSide side = SAME_EDGE; int u_out = -1; // Go up the cycle from source to the join node for (int u = source; u != join; u = node[u].parent) { int e = node[u].pred; bool edge_down = u == edge[e].node[1]; Flow d = edge_down ? edge[e].upper - edge[e].flow : edge[e].flow; if (flow_delta > d) { flow_delta = d; u_out = u; side = FIRST_SIDE; } } // Go up the cycle from target to the join node for (int u = target; u != join; u = node[u].parent) { int e = node[u].pred; bool edge_up = u == edge[e].node[0]; Flow d = edge_up ? edge[e].upper - edge[e].flow : edge[e].flow; if (flow_delta >= d) { flow_delta = d; u_out = u; side = SECOND_SIDE; } } // Put u_in on the same side as u_out u_in = side == FIRST_SIDE ? source : target; v_in = side == FIRST_SIDE ? target : source; // Augment along the cycle if (flow_delta) { auto delta = edge[in_arc].state * flow_delta; edge[in_arc].flow += delta; for (int u = edge[in_arc].node[0]; u != join; u = node[u].parent) { int e = node[u].pred; edge[e].flow += (u == edge[e].node[0] ? -1 : +1) * delta; } for (int u = edge[in_arc].node[1]; u != join; u = node[u].parent) { int e = node[u].pred; edge[e].flow += (u == edge[e].node[0] ? +1 : -1) * delta; } } if (side == SAME_EDGE) { edge[in_arc].state = ArcState(-edge[in_arc].state); return; } int out_arc = node[u_out].pred; edge[in_arc].state = STATE_TREE; edge[out_arc].state = edge[out_arc].flow ? STATE_UPPER : STATE_LOWER; int i = 0, S = 0; for (int u = u_in; u != u_out; u = node[u].parent) { bfs[S++] = u; } for (i = S - 1; i >= 0; i--) { int u = bfs[i], p = node[u].parent; children.erase(p); children.push_back(u, p); node[p].parent = u; node[p].pred = node[u].pred; } children.erase(u_in); children.push_back(v_in, u_in); node[u_in].parent = v_in; node[u_in].pred = in_arc; CostSum current_pi = reduced_cost(in_arc); CostSum pi_delta = (u_in == edge[in_arc].node[0] ? -1 : +1) * current_pi; assert(pi_delta != 0); bfs[0] = u_in; for (i = 0, S = 1; i < S; i++) { int u = bfs[i]; node[u].pi += pi_delta; FOR_EACH_IN_LINKED_LIST (v, u, children) { bfs[S++] = v; } } } }; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; using pcc = pair; using pii = pair; using pll = pair; using pdd = pair; using tuplis = array; template using pq = priority_queue, greater>; const ll LINF=0x1fffffffffffffff; const ll MINF=0x7fffffffffff; const int INF=0x3fffffff; const int MOD=1000000007; const int MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1}; const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1}; #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll i=0;i(a);) #define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each1(i,a) for(auto&&i:a) #define each2(x,y,a) for(auto&&[x,y]:a) #define each3(x,y,z,a) for(auto&&[x,y,z]:a) #define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) (i).rbegin(),(i).rend() #define rall2(i,k) (i).rbegin(),(i).rbegin()+k #define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) #define dsum(...) accumulate(all(__VA_ARGS__),0.0L) #define Msum(...) accumulate(all(__VA_ARGS__),0_M) #define elif else if #define unless(a) if(!(a)) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } inline ll popcnt(ull a){ return __builtin_popcountll(a); } ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } template bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; } template bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; } template bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; } template bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; } vector iota(ll n, ll begin = 0){ vector a(n); iota(a.begin(), a.end(), begin); return a; } vector factor(ull x){ vector ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } map factor_map(ull x){ map ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; } vector divisor(ull x){ vector ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } template unordered_map press(vector a){ Uniq(a); unordered_map ans; rep(a.size()) ans[a[i]] = i; return ans; } template map press_map(vector a){ Uniq(a); map ans; rep(a.size()) ans[a[i]] = i; return ans; } int scan(){ return getchar(); } void scan(int& a){ scanf("%d", &a); } void scan(unsigned& a){ scanf("%u", &a); } void scan(long& a){ scanf("%ld", &a); } void scan(long long& a){ scanf("%lld", &a); } void scan(unsigned long long& a){ scanf("%llu", &a); } void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); } void scan(float& a){ scanf("%f", &a); } void scan(double& a){ scanf("%lf", &a); } void scan(long double& a){ scanf("%Lf", &a); } void scan(vector& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto&& i : a) scan(i); } template void scan(deque& a){ for(auto&& i : a) scan(i); } template void scan(array& a){ for(auto&& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto&& i : a) scan(i); } template void scan(T& a){ cin >> a; } void in(){} template void in(T&... a){ (void)initializer_list{ (scan(a), 0)... }; } void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(unsigned a){ printf("%u", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(unsigned long long a){ printf("%llu", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(float a){ printf("%.15f", a); } void print(double a){ printf("%.15f", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } template void print(const complex& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); } template void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const pair& p){ print(p.first); putchar(' '); print(p.second); } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } #ifdef DEBUG inline ll __lg(ull x){ return 63 - __builtin_clzll(x); } #define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) void(0) #endif int first(bool i = true){ return out(i?"first":"second"); } int First(bool i = true){ return out(i?"First":"Second"); } int yes(bool i = true){ return out(i?"yes":"no"); } int Yes(bool i = true){ return out(i?"Yes":"No"); } int No(){ return out("No"); } int YES(bool i = true){ return out(i?"YES":"NO"); } int NO(){ return out("NO"); } int Yay(bool i = true){ return out(i?"Yay!":":("); } int possible(bool i = true){ return out(i?"possible":"impossible"); } int Possible(bool i = true){ return out(i?"Possible":"Impossible"); } int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); } void Case(ll i){ printf("Case #%lld: ", i); } int main(){ LL(n,m,k,l); const ll S=n+m; network_simplexg(S+1); rep(n)g.add_supply(i,1); rep(i,n,S)g.add_supply(i,-1); g.add_supply(S,m-n); rep(n)g.add(i,S,0,1,0); rep(i,n,S)g.add(S,i,0,1,0); rep(l){ LL(x,y,z); x--; y+=n-1; g.add(x,y,0,1,-1LL<