#include // created [2019/12/20] 03:56:38 #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; using uint = unsigned int; using usize = std::size_t; using ll = long long; using ull = unsigned long long; using ld = long double; template using arr = T (&)[n]; template using c_arr = const T (&)[n]; template constexpr T popcount(const T u) { return u ? static_cast(__builtin_popcountll(static_cast(u))) : static_cast(0); } template constexpr T log2p1(const T u) { return u ? static_cast(64 - __builtin_clzll(static_cast(u))) : static_cast(0); } template constexpr T msbp1(const T u) { return log2p1(u); } template constexpr T lsbp1(const T u) { return __builtin_ffsll(u); } template constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast(u); } template constexpr bool ispow2(const T u) { return u and (static_cast(u) & static_cast(u - 1)) == 0; } template constexpr T ceil2(const T u) { return static_cast(1) << clog(u); } template constexpr T floor2(const T u) { return u == 0 ? static_cast(0) : static_cast(1) << (log2p1(u) - 1); } template constexpr bool btest(const T mask, const usize ind) { return static_cast((static_cast(mask) >> ind) & static_cast(1)); } template void bset(T& mask, const usize ind) { mask |= (static_cast(1) << ind); } template void breset(T& mask, const usize ind) { mask &= ~(static_cast(1) << ind); } template void bflip(T& mask, const usize ind) { mask ^= (static_cast(1) << ind); } template void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); } template constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast(0) : static_cast((static_cast(mask) << (64 - ind)) >> (64 - ind)); } template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } constexpr unsigned int mod = 1000000007; template constexpr T inf_v = std::numeric_limits::max() / 4; template constexpr Real pi_v = Real{3.141592653589793238462643383279502884}; auto mfp = [](auto&& f) { return [=](auto&&... args) { return f(f, std::forward(args)...); }; }; template T in() { T v; return std::cin >> v, v; } template T in_v(typename std::enable_if<(i == n), c_arr>::type) { return in(); } template auto in_v(typename std::enable_if<(i < n), c_arr>::type& szs) { const usize s = (usize)szs[i]; std::vector(szs))> ans(s); for (usize j = 0; j < s; j++) { ans[j] = in_v(szs); } return ans; } template auto in_v(c_arr szs) { return in_v(szs); } template auto in_t() { return std::tuple...>{in()...}; } struct io_init { io_init() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(20); } void clear() { std::cin.tie(), std::ios::sync_with_stdio(true); } } io_setting; template int out(const T& v) { return std::cout << v, 0; } template int out(const std::vector& v) { for (usize i = 0; i < v.size(); i++) { if (i > 0) { std::cout << ' '; } out(v[i]); } return std::cout << "\n", 0; } template int out(const std::pair& v) { return out(v.first), std::cout << ' ', out(v.second), 0; } template int out(const T& v, const Args... args) { return out(v), std::cout << ' ', out(args...), 0; } template int outln(const Args... args) { return out(args...), std::cout << '\n', 0; } template void outel(const Args... args) { return out(args...), std::cout << std::endl, 0; } # define SHOW(...) static_cast(0) constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; } template auto make_v(typename std::enable_if<(i == n), c_arr>::type, const T& v = T{}) { return v; } template auto make_v(typename std::enable_if<(i < n), c_arr>::type szs, const T& v = T{}) { const usize s = (usize)szs[i]; return std::vector(szs, v))>(s, make_v(szs, v)); } template auto make_v(c_arr szs, const T& t = T{}) { return make_v(szs, t); } using namespace std; class Stack { private: const int N, H; vector node; public: Stack(const int _N, const int _H) : N(_N), H(_H), node(N + H) { clear(); } inline bool empty(const int h) const { return node[N + h] == N + h; } inline int top(const int h) const { return node[N + h]; } inline void pop(const int h) { node[N + h] = node[node[N + h]]; } inline void push(const int h, const int u) { node[u] = node[N + h], node[N + h] = u; } inline void clear() { iota(node.begin() + N, node.end(), N); } }; class List { public: struct node { int prev, next; }; const int N, H; vector sz; vector dat; List(const int _N, const int _H) : N(_N), H(_H), sz(H, 0), dat(N + H) { clear(); } inline size_t size(const int h) const { return sz[h]; } inline bool empty(const int h) const { return (sz[h] == 0); } inline void insert(const int h, const int u) { ++sz[h]; dat[u].prev = dat[N + h].prev, dat[u].next = N + h; dat[dat[N + h].prev].next = u, dat[N + h].prev = u; } inline void erase(const int h, const int u) { --sz[h]; dat[dat[u].prev].next = dat[u].next, dat[dat[u].next].prev = dat[u].prev; } inline void clear() { for (int i = N; i < N + H; ++i) dat[i].prev = dat[i].next = i; } }; template class PushRelabel { public: struct edge { const int to, rev; T cap; edge(const int _to, const int _rev, const T _cap) : to(_to), rev(_rev), cap(_cap) {} }; private: const int V; int s, t, pot_max, checker; vector excess; vector potential, cur_edge, que; List all_ver; Stack act_ver; int calc_active() { pot_max = -1; for (int i = 0; i < V; ++i) { if (potential[i] < V) { cur_edge[i] = 0; pot_max = max(potential[i], pot_max); all_ver.insert(potential[i], i); if (excess[i] > 0 && i != t) act_ver.push(potential[i], i); } else { potential[i] = V + 1; } } return pot_max; } void bfs() { for (int i = 0; i < V; ++i) potential[i] = max(potential[i], V); potential[t] = 0; int qh = 0, qt = 0; for (que[qt++] = t; qh++ < qt;) { int u = que[qh - 1]; for (const edge& e : G[u]) { if (potential[e.to] == V && G[e.to][e.rev].cap > 0) { potential[e.to] = potential[u] + 1, que[qt++] = e.to; } } } } int init() { potential[s] = V + 1; bfs(); for (edge& e : G[s]) { if (potential[e.to] < V) { G[e.to][e.rev].cap = e.cap, excess[s] -= e.cap, excess[e.to] += e.cap; } e.cap = 0; } return calc_active(); } int global_relabel() { bfs(); all_ver.clear(), act_ver.clear(); return calc_active(); } void gap_relabel(const int u) { for (int i = potential[u]; i <= pot_max; ++i) { for (int id = all_ver.dat[V + i].next; id < V; id = all_ver.dat[id].next) { potential[id] = V + 1; } all_ver.sz[i] = 0; all_ver.dat[V + i].prev = all_ver.dat[V + i].next = V + i; } } int discharge(const int u) { for (int& i = cur_edge[u]; i < (int)G[u].size(); ++i) { edge& e = G[u][i]; if (potential[u] == potential[e.to] + 1 && e.cap > 0) { if (push(u, e)) return potential[u]; } } return relabel(u); } bool push(const int u, edge& e) { T f = min(e.cap, excess[u]); const int v = e.to; e.cap -= f, excess[u] -= f; G[v][e.rev].cap += f, excess[v] += f; if (excess[v] == f && v != t) act_ver.push(potential[v], v); return (excess[u] == 0); } int relabel(const int u) { ++checker; int prv = potential[u], cur = V; for (int i = 0; i < (int)G[u].size(); ++i) { const edge& e = G[u][i]; if (cur > potential[e.to] + 1 && e.cap > 0) { cur_edge[u] = i; cur = potential[e.to] + 1; } } if ((int)all_ver.size(prv) > 1) { all_ver.erase(prv, u); if ((potential[u] = cur) == V) return potential[u] = V + 1, prv; act_ver.push(cur, u); all_ver.insert(cur, u); pot_max = max(pot_max, cur); } else { gap_relabel(u); return pot_max = prv - 1; } return cur; } public: vector> G; PushRelabel(const int node_size) : V(node_size), pot_max(-1), checker(0), excess(V, (T)0), potential(V, 0), cur_edge(V), que(V), all_ver(V, V), act_ver(V, V), G(V) {} void add_edge(const int _from, const int _to, const T _cap) { G[_from].emplace_back(_to, (int)G[_to].size(), _cap); G[_to].emplace_back(_from, (int)G[_from].size() - 1, 0); } T solve(const int source, const int sink) { s = source, t = sink; int level = init(); while (level >= 0) { if (act_ver.empty(level)) { --level; continue; } int u = act_ver.top(level); act_ver.pop(level); if (excess[u] == 0) continue; level = discharge(u); if (checker >= V / 2) { level = global_relabel(); checker = 0; } } return excess[t]; } }; template struct Dinic { const flow_t INF; struct edge { int to; flow_t cap; int rev; bool isrev; int idx; }; vector> graph; vector min_cost, iter; Dinic(int V) : INF(inf_v), 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 bfs(int s, int t) { min_cost.assign(graph.size(), -1); queue 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 dfs(int idx, const int t, flow_t flow) { if (idx == t) return flow; for (int& i = iter[idx]; i < graph[idx].size(); i++) { edge& e = graph[idx][i]; if (e.cap > 0 && min_cost[idx] < min_cost[e.to]) { flow_t d = dfs(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 (bfs(s, t)) { iter.assign(graph.size(), 0); flow_t f = 0; while ((f = dfs(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; } } } }; // template // struct PushRelabel // { // const flow_t INF; // struct edge // { // int to; // flow_t cap; // int rev; // bool isrev; // int idx; // }; // vector> graph; // vector ex; // int relabels, high; // vector cnt, h; // vector> hs; // PushRelabel(int V) : INF(inf_v), graph(V), high(0), hs(V + 1) {} // 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}); // } // void update_height(int idx, int nxt_height) // { // ++relabels; // if (h[idx] != graph.size() + 1) { // --cnt[h[idx]]; // } // h[idx] = nxt_height; // if (h[idx] != graph.size() + 1) { // high = nxt_height; // ++cnt[nxt_height]; // if (ex[idx] > 0) hs[nxt_height].emplace_back(idx); // } // } // void global_relabel(int idx) // { // for (int i = 0; i <= high; i++) hs[i].clear(); // relabels = 0; // high = 0; // h.assign(graph.size(), graph.size() + 1); // cnt.assign(graph.size(), 0); // queue que; // que.emplace(idx); // h[idx] = 0; // while (que.size()) { // int p = que.front(); // que.pop(); // for (auto& e : graph[p]) { // if (h[e.to] == graph.size() + 1 && graph[e.to][e.rev].cap > 0) { // que.emplace(e.to); // high = h[p] + 1; // update_height(e.to, high); // } // } // } // } // void push(int idx, edge& e) // { // if (h[e.to] == graph.size() + 1) return; // if (ex[e.to] == 0) { // hs[h[e.to]].emplace_back(e.to); // } // flow_t df = min(ex[idx], e.cap); // e.cap -= df; // graph[e.to][e.rev].cap += df; // ex[idx] -= df; // ex[e.to] += df; // } // void discharge(int idx) // { // int next_height = (int)graph.size() + 1; // for (auto&& e : graph[idx]) { // if (e.cap > 0) { // if (h[idx] == h[e.to] + 1) { // push(idx, e); // if (ex[idx] <= 0) return; // } else { // next_height = min(next_height, h[e.to] + 1); // } // } // } // if (cnt[h[idx]] > 1) { // update_height(idx, next_height); // } else { // for (; high >= h[idx]; hs[high--].clear()) { // for (int j : hs[high]) update_height(j, graph.size() + 1); // } // } // } // flow_t max_flow(int s, int t) // { // ex.assign(graph.size(), 0); // ex[s] = INF; // ex[t] = -INF; // global_relabel(t); // for (auto& e : graph[s]) push(s, e); // for (; high >= 0; high--) { // while (!hs[high].empty()) { // int idx = hs[high].back(); // hs[high].pop_back(); // discharge(idx); // if (relabels >= graph.size() * 4) global_relabel(t); // } // } // return ex[t] + INF; // } // 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; // } // } // } // }; int main() { const auto [H, W] = in_t(); const auto G = in_v({H, W}); auto R = in_v({H}); auto C = in_v({W}); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { R[i] -= G[i][j]; C[j] -= G[i][j]; } } constexpr ll inf = TEN(9); PushRelabel f(H * W + H + W + 2); // Dinic f(H * W + H + W + 2); const int S = H * W + H + W; const int T = H * W + H + W + 1; ll ans = 0; for (int i = 0; i < H; i++) { if (R[i] < 0) { f.add_edge(i, T, -R[i]); } else { ans += R[i]; } } for (int j = 0; j < W; j++) { if (C[j] < 0) { f.add_edge(H + j, T, -C[j]); } else { ans += C[j]; } } for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { const int v = i * W + j + H + W; if (R[i] < 0) { f.add_edge(v, i, inf); } if (C[j] < 0) { f.add_edge(v, H + j, inf); } ans += G[i][j]; if (R[i] < 0 or C[j] < 0) { f.add_edge(S, v, G[i][j]); } } } SHOW(ans); outln(ans - f.solve(S, T)); return 0; }