#include using namespace std; using int64 = long long; const int mod = 1e9 + 7; //const int mod = 998244353; 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)}; } #line 2 "graph/flow/burn-bury.hpp" #line 2 "structure/union-find/union-find.hpp" /** * @brief Union-Find * @docs docs/union-find.md */ struct UnionFind { vector< int > data; UnionFind() = default; explicit UnionFind(size_t sz) : data(sz, -1) {} bool unite(int x, int y) { x = find(x), y = find(y); if(x == y) return false; if(data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return true; } int find(int k) { if(data[k] < 0) return (k); return data[k] = find(data[k]); } int size(int k) { return -data[find(k)]; } bool same(int x, int y) { return find(x) == find(y); } vector< vector< int > > groups() { int n = (int) data.size(); vector< vector< int > > ret(n); for(int i = 0; i < n; i++) { ret[find(i)].emplace_back(i); } ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) { return v.empty(); }), end(ret)); return ret; } }; #line 1 "graph/flow/dinic.hpp" /** * @brief Dinic(最大流) * @docs docs/dinic.md */ template< typename flow_t > struct Dinic { const flow_t INF; struct edge { int to; flow_t cap; int rev; bool isrev; int idx; }; vector< vector< edge > > graph; vector< int > min_cost, iter; explicit Dinic(int V) : INF(numeric_limits< flow_t >::max()), graph(V) {} void add_edge(int from, int to, flow_t cap, int idx = -1) { graph[from].emplace_back((edge) {to, cap, (int) graph[to].size(), false, idx}); graph[to].emplace_back((edge) {from, 0, (int) graph[from].size() - 1, true, idx}); } bool build_augment_path(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) { min_cost[e.to] = min_cost[p] + 1; que.push(e.to); } } } return min_cost[t] != -1; } flow_t find_min_dist_augment_path(int idx, const int t, flow_t flow) { if(idx == t) return flow; for(int &i = iter[idx]; i < (int) graph[idx].size(); i++) { edge &e = graph[idx][i]; if(e.cap > 0 && min_cost[idx] < min_cost[e.to]) { flow_t d = find_min_dist_augment_path(e.to, t, min(flow, e.cap)); if(d > 0) { e.cap -= d; graph[e.to][e.rev].cap += d; return d; } } } return 0; } flow_t max_flow(int s, int t) { flow_t flow = 0; while(build_augment_path(s, t)) { iter.assign(graph.size(), 0); flow_t f; while((f = find_min_dist_augment_path(s, t, INF)) > 0) flow += f; } return flow; } 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; } } } vector< bool > min_cut(int s) { vector< bool > used(graph.size()); queue< int > que; que.emplace(s); used[s] = true; while(not que.empty()) { int p = que.front(); que.pop(); for(auto &e: graph[p]) { if(e.cap > 0 and not used[e.to]) { used[e.to] = true; que.emplace(e.to); } } } return used; } }; #line 5 "graph/flow/burn-bury.hpp" /** * @brief Burn Bury(燃やす埋める) */ template< typename T, bool minimize = true > struct BurnBury { private: using MaxFlow = Dinic< T >; using UF = UnionFind; using arr2 = array< T, 2 >; using arr4 = array< T, 4 >; int n; T alpha; vector< arr2 > theta; vector< map< int, arr4 > > phi; map< vector< int >, T > zeta; public: explicit BurnBury(int n) : n{n}, alpha{}, theta(n), phi(n) {} void add_cost(T cost) { if(not minimize) cost *= -1; alpha += cost; } void add_cost(int x, T cost) { if(not minimize) cost *= -1; int a = max(~x, x); theta[a][x >= 0] += cost; } void add_cost(int x, int y, T cost) { assert(x != y); if(not minimize) cost *= -1; int a = max(~x, x), b = max(~y, y); if(a < b) phi[a][b][((x >= 0) << 1) | (y >= 0)] += cost; else phi[b][a][((y >= 0) << 1) | (x >= 0)] += cost; } void add_cost(vector< int > xs, T cost) { assert(not xs.empty()); if(xs.size() == 1) { add_cost(xs[0], cost); } else if(xs.size() == 2) { add_cost(xs[0], xs[1], cost); } else { int m = (int) xs.size(); sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end()); assert(m == (int) xs.size()); if(not minimize) cost *= -1; zeta[xs] += cost; } } optional< pair< T, vector< bool > > > solve() { vector< int > flip(2 * n, -1); { UF uf(n + n); for(int i = 0; i < n; i++) { for(auto&[j, cs]: phi[i]) { T c = -cs[0] + cs[1] + cs[2] - cs[3]; if(c < 0) { uf.unite(i, j + n); uf.unite(i + n, j); } else if(c > 0) { uf.unite(i, j); uf.unite(i + n, j + n); } } } for(auto&[vs, c]: zeta) { if(c > 0) return nullopt; if(c < 0) { for(int i = 1; i < (int) vs.size(); i++) { int x = vs[i - 1], y = vs[i]; int a = max(x, ~x), b = max(y, ~y); if((x >= 0) ^ (y >= 0)) { uf.unite(a, b + n); uf.unite(a + n, b); } else { uf.unite(a, b); uf.unite(a + n, b + n); } } } } for(int i = 0; i < n; i++) { int x = uf.find(i); int y = uf.find(i + n); if(x == y) return nullopt; if(flip[x] < 0) { flip[x] = 0; flip[y] = 1; } } for(int i = 0; i < n; i++) { if(flip[i] < 0) { flip[i] = flip[uf.find(i)]; } } flip.resize(n); } { for(int i = 0; i < n; i++) { for(auto&[j, cs]: phi[i]) { if(flip[i]) { swap(cs[0], cs[2]); swap(cs[1], cs[3]); } if(flip[j]) { swap(cs[0], cs[1]); swap(cs[2], cs[3]); } T c = -cs[0] + cs[1] + cs[2] - cs[3]; alpha += cs[0]; theta[i][not flip[i]] += cs[2] - cs[0]; theta[j][not flip[j]] += cs[3] - cs[2]; cs[1] = c; cs[0] = cs[2] = cs[3] = 0; } } } { for(int i = 0; i < n; i++) { auto &cs = theta[i]; if(flip[i]) { swap(cs[0], cs[1]); } if(cs[0] <= cs[1]) { alpha += cs[0]; cs[1] -= cs[0]; cs[0] = 0; } else { alpha += cs[1]; cs[0] -= cs[1]; cs[1] = 0; } } } MaxFlow flow(n + 2 + zeta.size()); int s = n, t = n + 1; { for(int i = 0; i < n; i++) { auto &cs = theta[i]; if(cs[1] > 0) { flow.add_edge(i, t, cs[1]); } if(cs[0] > 0) { flow.add_edge(s, i, cs[0]); } } for(int i = 0; i < n; i++) { for(auto&[j, cs]: phi[i]) { if(cs[2] > 0) { flow.add_edge(i, j, cs[2]); } if(cs[1] > 0) { flow.add_edge(j, i, cs[1]); } } } int u = t + 1; for(auto&[vs, c]: zeta) { if(c < 0) { if((vs[0] >= 0) ^ flip[max(~vs[0], vs[0])]) { flow.add_edge(s, u, -c); for(auto &p: vs) flow.add_edge(u, max(p, ~p), -c); } else { for(auto &p: vs) flow.add_edge(max(p, ~p), u, -c); flow.add_edge(u, t, -c); } alpha += c; u++; } } } T ans = flow.max_flow(s, t) + alpha; vector< bool > cut = flow.min_cut(s); for(int i = 0; i < n; i++) { if(flip[i]) cut[i] = 1 - cut[i]; } cut.resize(n); return make_pair(minimize ? ans : -ans, cut); } }; int main() { int H, W; cin >> H >> W; auto G = make_v< int >(H, W); cin >> G; vector< int > R(H), C(W); cin >> R >> C; BurnBury< int64, false > flow(H + W); for(int i = 0; i < H; i++) { for(int j = 0; j < W; j++) { flow.add_cost(i, ~(j + H), -G[i][j]); flow.add_cost(~i, j + H, -G[i][j]); flow.add_cost(i, j + H, -G[i][j]); } } for(int i = 0; i < H; i++) { flow.add_cost(i, R[i]); } for(int i = 0; i < W; i++) { flow.add_cost(i + H, C[i]); } cout << flow.solve().value().first << "\n"; }