/** * @FileName a.cpp * @Author kanpurin * @Created 2022.06.21 01:26:34 **/ #include "bits/stdc++.h" using namespace std; typedef long long ll; struct Dinic { private: struct edge { int to; ll cap; int rev; bool isrev; int idx; }; vector< vector< edge > > graph; vector< int > min_cost, iter; bool bfs(int s, int t) { min_cost.assign(graph.size(), -1); queue< int > que; min_cost[s] = 0; que.push(s); while (!que.empty() && min_cost[t] == -1) { int p = que.front(); que.pop(); for (auto &e : graph[p]) { if (e.cap == 0 || min_cost[e.to] != -1) continue; min_cost[e.to] = min_cost[p] + 1; que.push(e.to); } } return min_cost[t] != -1; } ll dfs(const int s, int v, ll flow) { if (v == s) return flow; ll res = 0; int min_cost_v = min_cost[v]; for (int &i = iter[v]; i < (int)graph[v].size(); i++) { edge &e = graph[v][i]; if (graph[e.to][e.rev].cap == 0 || min_cost_v <= min_cost[e.to]) continue; ll d = dfs(s, e.to, min(flow-res, graph[e.to][e.rev].cap)); if (d <= 0) continue; e.cap += d; graph[e.to][e.rev].cap -= d; res += d; if (res == flow) return res; } min_cost[v] = (int)graph.size(); return res; } public: Dinic() {} Dinic(int V) : graph(V) {} void add_edge(int from, int to, ll cap, int idx = -1) { graph[from].push_back({to, cap, (int)graph[to].size(), false, idx}); graph[to].push_back({from, 0, (int)graph[from].size() - 1, true, idx}); } ll max_flow(int s, int t, ll flow_limit = 1e18 + 6) { ll flow = 0; while (bfs(s, t)) { if (min_cost[t] == -1) break; iter.assign(graph.size(), 0); ll f = dfs(s, t, flow_limit-flow); if (!f) break; flow += f; } return flow; } vector min_cnt(int s,int t) { vector visited(graph.size()); vector ret; stack sta; visited[s] = true; sta.push(s); ret.push_back(s); while(!sta.empty()) { int v = sta.top(); sta.pop(); for (auto &e : graph[v]) { if (visited[e.to] || e.cap == 0) continue; visited[e.to] = true; sta.push(e.to); ret.push_back(e.to); } } return ret; } void output() { for (int i = 0; i < graph.size(); i++) { for (auto &e : graph[i]) { if (e.isrev) continue; auto &rev_e = graph[e.to][e.rev]; cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << e.cap + rev_e.cap << ")" << endl; } } } }; struct ProjectSelectionProblem { const long long INF = 1e18+1; int n; vector k; vector s; vector> cost; Dinic G; long long ans; ProjectSelectionProblem(vector k) : k(k) { n = k.size(); s = vector(n+1); s[0] = 0; for (int i = 0; i < n; i++) { assert(k[i] >= 2); s[i+1] = s[i]+k[i]-1; } cost = vector>(n); for (int i = 0; i < n; i++) cost[i] = vector(k[i],0); G = Dinic(s[n]+2); ans = 0; } void add_cost_1(int a,vector x) { assert(0 <= a && a < n); assert(k[a] == (int)x.size()); for (int i = 0; i < k[a]; i++) { cost[a][i] += x[i]; } } void add_cost_2(int a,int b,vector> x) { assert(0 <= a && a < n && 0 <= b && b < n); assert((int)x.size() == k[a]); for (int i = 0; i < k[a]; i++) { assert((int)x[i].size() == k[b]); cost[a][i] += x[i][0]; for (int j = k[b]-1; j >= 0; j--) x[i][j] -= x[i][0]; } for (int i = 1; i < k[b]; i++){ cost[b][i] += x[k[a]-1][i]; for (int j = 0; j < k[a]; j++) x[j][i] -= x[k[a]-1][i]; } for (int i = 0; i < k[a]-1; i++){ for (int j = 0; j < k[b]-1; j++){ long long c = x[i+1][j]+x[i][j+1]-x[i][j]-x[i+1][j+1]; assert(c >= 0); if (c == 0) continue; G.add_edge(s[b]+j, s[a]+i, c); } } } long long mincost() { for (int i = 0; i < n; i++){ for (int j = 0; j < k[i]-2; j++) G.add_edge(s[i]+j+1, s[i]+j, INF); ans += cost[i][k[i]-1]; for (int j = 0; j < k[i]-1; j++){ if (cost[i][j] > cost[i][j+1]) { G.add_edge(s[n], s[i]+j, cost[i][j]-cost[i][j+1]); } else { G.add_edge(s[i]+j, s[n]+1, cost[i][j+1]-cost[i][j]); ans -= cost[i][j+1]-cost[i][j]; } } } return ans+G.max_flow(s[n], s[n]+1); } vector answer() { vector ans(n); auto v = G.min_cnt(s[n],s[n]+1); vector scut(s[n]+2); for (int i = 0; i < v.size(); i++) scut[v[i]] = true; for (int i = 0; i < n; i++) { for (int j = 0; j < k[i]-1; j++) { if (!scut[s[i]+j]) { ans[i] = j; break; } else if (j == k[i]-2) { ans[i] = k[i]-1; } } } return ans; } }; int main() { int n,m,k,p;cin >> n >> m >> k >> p; ProjectSelectionProblem psp(vector(n+m+k,2)); vector (); for (int i = 0; i < n; i++) { vector cost1(2); cin >> cost1[0]; cost1[0] *= -1; psp.add_cost_1(i,cost1); } for (int i = 0; i < m; i++) { vector cost1(2); cin >> cost1[1]; cost1[1] *= -1; psp.add_cost_1(i+n,cost1); } for (int i = 0; i < k; i++) { vector cost1(2); cin >> cost1[0]; psp.add_cost_1(i+n+m,cost1); } for (int i = 0; i < n; i++) { int L;cin >> L; for (int j = 0; j < L; j++) { int a;cin >> a; vector> cost2(2,vector(2)); cost2[0][1] = 1e10; psp.add_cost_2(i,a-1+n+m,cost2); } } for (int i = 0; i < p; i++) { int x,y;cin >> x >> y; x = x-1; y = n+y-1; vector> cost2(2,vector(2)); cost2[0][1] = 1e10; psp.add_cost_2(x,y,cost2); } cout << -psp.mincost() << endl; auto ans = psp.answer(); vector> ans2; for (int i = 0; i < k; i++) { if (ans[n+m+i] == 0) ans2.push_back({"Preparation",i+1}); } for (int i = 0; i < n; i++) { if (ans[i] == 0) ans2.push_back({"Goal",i+1}); } for (int i = 0; i < m; i++) { if (ans[n+i] == 1) ans2.push_back({"Action",i+1}); } cout << ans2.size() << endl; for (int i = 0; i < ans2.size(); i++) { cout << ans2[i].first << " " << ans2[i].second << endl; } return 0; }