#line 1 "/home/maspy/compro/library/my_template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using pi = pair; using vi = vector; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vec(type, name, ...) vector name(__VA_ARGS__) #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c)) #define overload4(a, b, c, d, e, ...) e #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) \ overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s)) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll template T SUM(const vector &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T pick(deque &que) { T a = que.front(); que.pop_front(); return a; } template T pick(pq &que) { T a = que.top(); que.pop(); return a; } template T pick(pqg &que) { assert(que.size()); T a = que.top(); que.pop(); return a; } template T pick(vc &que) { assert(que.size()); T a = que.back(); que.pop_back(); return a; } template T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template ll binary_search(F check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = S[i] - first_char; } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } template vc bincount(const vc &A, int size) { vc C(size); for (auto &&x: A) { ++C[x]; } return C; } // stable template vector argsort(const vector &A) { vector ids(A.size()); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { int n = len(I); vc B(n); FOR(i, n) B[i] = A[I[i]]; return B; } #line 1 "/home/maspy/compro/library/other/io.hpp" // based on yosupo's fastio #include namespace detail { template std::true_type check_value(int); template std::false_type check_value(long); } // namespace detail template struct is_modint : decltype(detail::check_value(0)) {}; template using is_modint_t = enable_if_t::value>; template using is_not_modint_t = enable_if_t::value>; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template * = nullptr> bool read_single(T &ref) { long long val = 0; bool f = read_single(val); ref = T(val); return f; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template bool read_single(vector &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template bool read_single(pair &p) { return (read_single(p.first) && read_single(p.second)); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p))); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p)) && read_single(get<3>(p))); } void read() {} template void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char &val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string &s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template * = nullptr> void write(T &ref) { write(ref.val); } template void write(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template void write(const pair &val) { write(val.first); write(' '); write(val.second); } template void write(const tuple &val) { auto &[a, b, c] = val; write(a), write(' '), write(b), write(' '), write(c); } template void write(const tuple &val) { auto &[a, b, c, d] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d); } template void write(const tuple &val) { auto &[a, b, c, d, e] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e); } template void write(const tuple &val) { auto &[a, b, c, d, e, f] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f); } template void write(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if(val < 0){ negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if(negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward(tail)...); } void read() {} template void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 1 "/home/maspy/compro/library/flow/maxflow.hpp" template struct MaxFlowGraph { struct Edge { int to, rev; Cap cap; }; const Cap INF; int N; vvc G; vc prog, level; Cap flow_ans; bool calculated; MaxFlowGraph(int N, Cap INF) : INF(INF), N(N), calculated(0) {} void add(int frm, int to, Cap cap) { assert(0 <= frm && frm < N); assert(0 <= to && to < N); assert(Cap(0) <= cap); if (len(G) < N) G.resize(N); G[frm].eb(Edge{to, (int)G[to].size(), cap}); G[to].eb(Edge{frm, (int)G[frm].size() - 1, 0}); } Cap flow(int source, int sink) { if (calculated) return flow_ans; calculated = true; chmax(N, source + 1); chmax(N, sink + 1); G.resize(N); flow_ans = 0; while (set_level(source, sink)) { fill(all(prog), 0); prog.assign(N, 0); while (1) { Cap x = flow_dfs(source, sink, INF); if (x == 0) break; flow_ans += x; chmin(flow_ans, INF); if (flow_ans == INF) return flow_ans; } } return flow_ans; } // 最小カットの値および、カットを表す 01 列を返す pair> cut(int source, int sink) { Cap f = flow(source, sink); vc res(N); FOR(v, N) res[v] = (level[v] >= 0 ? 0 : 1); return {f, res}; } // 残余グラフの辺 vc> get_edges() { vc> edges; FOR(v, N) for (auto&& e: G[v]) { edges.eb(v, e.to, e.cap); } return edges; } private: bool set_level(int source, int sink) { level.assign(N, -1); level[source] = 0; queue que; que.push(source); while (!que.empty()) { int v = que.front(); que.pop(); for (auto&& e: G[v]) { if (e.cap > 0 && level[e.to] == -1) { level[e.to] = level[v] + 1; if (e.to == sink) return true; que.push(e.to); } } } return false; } Cap flow_dfs(int v, int sink, Cap lim) { if (v == sink) return lim; Cap res = 0; for (int& i = prog[v]; i < (int)G[v].size(); ++i) { auto& e = G[v][i]; if (e.cap > 0 && level[e.to] == level[v] + 1) { Cap a = flow_dfs(e.to, sink, min(lim, e.cap)); if (a > 0) { e.cap -= a; G[e.to][e.rev].cap += a; res += a; lim -= a; if (lim == 0) break; } } } return res; } }; #line 2 "/home/maspy/compro/library/flow/binary_optimization.hpp" template struct Binary_Optimization { int n; int nxt; int source, sink; T base_cost; T INF; map, T> edges; Binary_Optimization(int n, T INF) : n(n), base_cost(0), INF(INF) { source = n; sink = n + 1; nxt = n + 2; } // xi を 0, 1 にするときにかかるコストを追加する。 void add_1(int i, T x0, T x1) { assert(0 <= i && i < n); if (!MINIMIZE) { x0 = -x0, x1 = -x1; } _add_1(i, x0, x1); } // (xi,xj) = (00,01,10,11) とするときにかかるコストを追加する。 // コストが劣モ x00 + x11 <= x10 + x10 になっている必要がある。 // 特に、対角成分に利得を与えることができる。 void add_2(int i, int j, T x00, T x01, T x10, T x11) { assert(i != j); assert(0 <= i && i < n); assert(0 <= j && j < n); if (!MINIMIZE) { x00 = -x00, x01 = -x01; x10 = -x10, x11 = -x11; } _add_2(i, j, x00, x01, x10, x11); } // (xi,xj,xk) = (000,001,010,011,100,101,110,111) // とするときにかかるコストを追加する。劣モになっている必要がある。 // 特に、000 や 111 に利得を与えることができる。 void add_3(int i, int j, int k, T x000, T x001, T x010, T x011, T x100, T x101, T x110, T x111) { assert(i != j && i != k && j != k); assert(0 <= i && i < n); assert(0 <= j && j < n); assert(0 <= k && k < n); if (!MINIMIZE) { x000 = -x000, x001 = -x001; x010 = -x010, x011 = -x011; x100 = -x100, x101 = -x101; x110 = -x110, x111 = -x111; } _add_3(i, j, k, x000, x001, x010, x011, x100, x101, x110, x111); } // 最小値および、01 列を返す pair> calc() { MaxFlowGraph G(nxt, INF); for (auto&& [key, cap]: edges) { auto [frm, to] = key; G.add(frm, to, cap); } auto [val, cut] = G.cut(source, sink); val += base_cost; chmin(val, INF); cut.resize(n); if (!MINIMIZE) val = -val; return {val, cut}; } void debug() { print("base_cost", base_cost); print("source=", source, "sink=", sink); for (auto&& [key, cap]: edges) print(key, cap); } private: void add_edge(int i, int j, T t) { assert(t >= 0); if (t == 0) return; pair key = mp(i, j); edges[key] += t; chmin(edges[key], INF); } void _add_1(int i, T x0, T x1) { if (x0 <= x1) { base_cost += x0; add_edge(source, i, x1 - x0); } else { base_cost += x1; add_edge(i, sink, x0 - x1); } } void _add_2(int i, int j, T x00, T x01, T x10, T x11) { assert(x00 + x11 <= x01 + x10); _add_1(i, x00, x10); _add_1(j, 0, x11 - x10); add_edge(i, j, x01 + x10 - x00 - x11); } void _add_3(int i, int j, int k, T x000, T x001, T x010, T x011, T x100, T x101, T x110, T x111) { T p = x000 - x100 - x010 - x001 + x110 + x101 + x011 - x111; if (p > 0) { base_cost += x000; _add_1(i, 0, x100 - x000); _add_1(j, 0, x010 - x000); _add_1(k, 0, x001 - x000); _add_2(i, j, 0, 0, 0, x000 + x110 - x100 - x010); _add_2(i, k, 0, 0, 0, x000 + x101 - x100 - x001); _add_2(j, k, 0, 0, 0, x000 + x011 - x010 - x001); // あとは、111 のときに利得 p を追加する base_cost -= p; // 111 以外だとコスト p add_edge(i, nxt, p); add_edge(j, nxt, p); add_edge(k, nxt, p); add_edge(nxt, sink, p); ++nxt; } else { p = -p; base_cost += x111; _add_1(i, x011 - x111, 0); _add_1(i, x101 - x111, 0); _add_1(i, x110 - x111, 0); _add_2(i, j, x111 + x001 - x011 - x101, 0, 0, 0); _add_2(i, k, x111 + x010 - x011 - x110, 0, 0, 0); _add_2(j, k, x111 + x100 - x101 - x110, 0, 0, 0); // 000 のときに利得 p を追加する base_cost -= p; // 000 以外だとコスト p add_edge(nxt, i, p); add_edge(nxt, j, p); add_edge(nxt, k, p); add_edge(source, nxt, p); ++nxt; } } }; #line 4 "main.cpp" void solve() { ll C = 1LL << 50; const ll INF = 1LL << 60; LL(N, M, K, P); VEC(ll, E, N); VEC(ll, F, M); VEC(ll, V, K); Binary_Optimization X(N + M + K, INF); /* 目標:[0,N)、やるのが 1 行動:[N,N+M)、やるのが 0 準備:[N+M,N+M+K)、やるのが 1 */ FOR(i, N) { LL(L); FOR(L) { LL(a); --a; a += N + M; X.add_2(a, i, 0, -C, 0, 0); } } FOR(i, N) X.add_1(i, 0, E[i]); FOR(j, M) X.add_1(N + j, F[j], 0); FOR(k, K) X.add_1(N + M + k, 0, -V[k]); FOR(P) { LL(i, j); --i, --j; X.add_2(i, N + j, 0, 0, -C, 0); } auto [val, x] = X.calc(); { vi A, B, C; FOR(i, N) if (x[i]) A.eb(1 + i); FOR(j, M) if (!x[N + j]) B.eb(1 + j); FOR(k, K) if (x[N + M + k]) C.eb(k); print(val); print(len(A) + len(B) + len(C)); for (auto&& x: C) { print("Preparation", x); } for (auto&& x: A) { print("Goal", x); } for (auto&& x: B) { print("Action", x); } } } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }