#include #ifdef LOCAL #include #else #define debug(...) void(0) #endif namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace ProjectSelectionProblem_Impl { template struct mf_graph { public: mf_graph() : _n(0) {} explicit mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } int add_vertex() { g.resize(_n + 1); return _n++; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); atcoder::internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); atcoder::internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; template struct ProjectSelectionProblem { ProjectSelectionProblem(int n) : n(n + 2), s(n), t(n + 1), sum(T(0)), graph(n + 2) {} void x_false_loss(int x, T z) { assert(0 <= x and x < n); graph.add_edge(x, t, z); } void x_false_profit(int x, T z) { assert(0 <= x and x < n); sum += z; x_true_loss(x, z); } void x_true_loss(int x, T z) { assert(0 <= x and x < n); graph.add_edge(s, x, z); } void x_true_profit(int x, T z) { assert(0 <= x and x < n); sum += z; x_false_loss(x, z); } void x_false_y_true_loss(int x, int y, T z) { assert(0 <= x and x < n); assert(0 <= y and y < n); graph.add_edge(x, y, z); } void x_true_y_false_loss(int x, int y, T z) { assert(0 <= x and x < n); assert(0 <= y and y < n); graph.add_edge(y, x, z); } void x_false_y_false_profit(int x, int y, T z) { assert(0 <= x and x < n); assert(0 <= y and y < n); sum += z; int w = graph.add_vertex(); n++; x_true_loss(w, z); x_false_y_true_loss(w, x, inf); x_false_y_true_loss(w, y, inf); } void x_true_y_true_profit(int x, int y, T z) { assert(0 <= x and x < n); assert(0 <= y and y < n); sum += z; int w = graph.add_vertex(); n++; x_false_loss(w, z); x_true_y_false_loss(w, x, inf); x_true_y_false_loss(w, y, inf); } T min_loss() { return graph.flow(s, t) - sum; } T max_profit() { return -min_loss(); } private: int n, s, t; T sum; const T inf = std::numeric_limits::max() / 2; mf_graph graph; }; } // namespace ProjectSelectionProblem_Impl using ProjectSelectionProblem_Impl::ProjectSelectionProblem; using namespace std; typedef long long ll; #define all(x) begin(x), end(x) constexpr int INF = (1 << 30) - 1; constexpr long long IINF = (1LL << 60) - 1; constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; template istream& operator>>(istream& is, vector& v) { for (auto& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { auto sep = ""; for (const auto& x : v) os << exchange(sep, " ") << x; return os; } template bool chmin(T& x, U&& y) { return y < x and (x = forward(y), true); } template bool chmax(T& x, U&& y) { return x < y and (x = forward(y), true); } template void mkuni(vector& v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template int lwb(const vector& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N, S, T; cin >> N >> S >> T; vector E(S), R(T); for (int& x : E) cin >> x, x--; for (int& x : R) cin >> x, x--; vector C(N, vector(N)); cin >> C; vector idx(N, 0); for (int& x : E) idx[x] = -1; for (int& x : R) idx[x] = -2; vector rest; for (int i = 0; i < N; i++) { if (idx[i] == 0) { idx[i] = rest.size(); rest.emplace_back(i); } } int n = rest.size(); ProjectSelectionProblem PSP(n); ll ans = 0; for (int i = 0; i < S; i++) { for (int j = i + 1; j < S; j++) { ans += C[E[i]][E[j]]; } } for (int i = 0; i < T; i++) { for (int j = i + 1; j < T; j++) { ans += C[R[i]][R[j]]; } } for (int i = 0; i < N; i++) { if (idx[i] < 0) continue; for (int j = 0; j < N; j++) { if (idx[j] == -1) PSP.x_false_profit(idx[i], C[i][j]); else if (idx[j] == -2) PSP.x_true_profit(idx[i], C[i][j]); else if (i < j) { PSP.x_false_y_false_profit(idx[i], idx[j], C[i][j]); PSP.x_true_y_true_profit(idx[i], idx[j], C[i][j]); } } } ans += PSP.max_profit(); cout << ans << '\n'; return 0; }