/* #region Head */ // #define _GLIBCXX_DEBUG #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define endl '\n' #define sqrt sqrtl #define floor floorl #define log2 log2l constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ /* #region TreeDP */ template struct TreeDP { using merge_t = function; using add_root_t = function; struct edge_t { int to; ll cost; edge_t(int to, ll cost = 0) : to(to), cost(cost) {} }; using graph_t = vc>; merge_t merge; add_root_t add_root; int n; //木の要素数 const T e; //単位元 vector dp; graph_t G; TreeDP(merge_t merge, add_root_t add_root, int n, T e) : merge(merge), add_root(add_root), n(n), e(e) { dp.resize(n), G.resize(n); } void add_edge(int a, int b) { G[a].emplace_back(b); } void build() { dfs(0); } void dfs(int v, int p = -1) { T dp_cum = e; int deg = (int)G[v].size(); for (int i = 0; i < deg; ++i) { int x = G[v][i].to; if (x == p) continue; dfs(x, v); dp_cum = merge(dp_cum, dp[x], v, x); } dp[v] = add_root(dp_cum, v); } }; /* #endregion */ // Problem void solve() { ll n; cin >> n; vll a(n), b(n); cin >> a >> b; vll u(n - 1), v(n - 1); REP(i, 0, n - 1) { cin >> u[i] >> v[i]; --u[i], --v[i]; } // 消されている場合のスコアは,頂点追加時に加算する // 頂点が残っている場合のスコアは,部分木追加時に計算する using data = pair; // その頂点が消されている場合 / 残っている場合 のスコア auto merge = [&b](data dp_cum, data d, int v_parent, int v_child) -> data { auto [cum0, cum1] = dp_cum; auto [d0, d1] = d; // その部分木の頂点が消されている場合 / 残っている場合 のスコア // 頂点を残す場合,部分木が消えていたほうが得か,残っていた方が得かは,部分木ごとに決定可能 // 頂点を消す場合,部分木が残っているかどうかは関係ない return {cum0 + max(d0, d1), cum1 + max(d0, d1 + b[v_parent] + b[v_child])}; }; auto add_root = [&a](data d, int v) -> data { auto [d0, d1] = d; return {d0 + a[v], d1}; }; TreeDP tdp(merge, add_root, n, data({0, 0})); REP(i, 0, n - 1) { tdp.add_edge(u[i], v[i]); tdp.add_edge(v[i], u[i]); } tdp.build(); // dump(tdp.dp); // dump(tdp.dp[0]); cout << max(tdp.dp[0].first, tdp.dp[0].second) << endl; } // entry point int main() { solve(); return 0; }