#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)}; } template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } }; template< typename T = int > using Edges = vector< Edge< T > >; /** * @brief Slope-Trick * @docs docs/slope-trick.md * @see https://maspypy.com/slope-trick-1-%E8%A7%A3%E8%AA%AC%E7%B7%A8 */ template< typename T > struct LazySplayTree { public: struct Node { Node *l, *r, *p; T key; T val, sum; size_t sz; T add; bool is_root() const { return !p || (p->l != this && p->r != this); } Node(const T &key, const T &val, const T &add) : key(key), val(val), sum(val), sz(1), add(add), l(nullptr), r(nullptr), p(nullptr) {} }; LazySplayTree() = default; inline size_t count(const Node *t) { return t ? t->sz : 0; } Node *alloc(const T &key, const T &val, const T &add = T()) { return new Node(key, val, add); } void splay(Node *t) { push(t); while(!t->is_root()) { auto *q = t->p; if(q->is_root()) { push(q), push(t); if(q->l == t) rotr(t); else rotl(t); } else { auto *r = q->p; push(r), push(q), push(t); if(r->l == q) { if(q->l == t) rotr(q), rotr(t); else rotl(t), rotr(t); } else { if(q->r == t) rotl(q), rotl(t); else rotr(t), rotl(t); } } } } Node *erase(Node *t) { splay(t); Node *x = t->l, *y = t->r; delete t; if(!x) { t = y; if(t) t->p = nullptr; } else if(!y) { t = x; t->p = nullptr; } else { x->p = nullptr; t = get_right(x); splay(t); t->r = y; y->p = t; } return t; } Node *get_left(Node *t) const { while(t->l) t = t->l; return t; } Node *get_right(Node *t) const { while(t->r) t = t->r; return t; } void set_propagate(Node *t, const T &add) { splay(t); propagate(t, add); push(t); } pair< Node *, Node * > split(Node *t, int k) { if(!t) return {nullptr, nullptr}; push(t); if(k <= count(t->l)) { auto x = split(t->l, k); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split(t->r, k - count(t->l) - 1); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } tuple< Node *, Node *, Node * > split3(Node *t, int a, int b) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); return make_tuple(x.first, y.first, y.second); } pair< Node *, Node * > split_lower_bound(Node *t, const T &key) { if(!t) return {nullptr, nullptr}; push(t); if(key <= t->key) { auto x = split_lower_bound(t->l, key); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split_lower_bound(t->r, key); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } template< typename ... Args > Node *merge(Node *l, Args ...rest) { Node *r = merge(rest...); if(!l && !r) return nullptr; if(!l) return splay(r), r; if(!r) return splay(l), l; splay(l), splay(r); l = get_right(l); splay(l); l->r = r; r->p = l; update(l); return l; } Node *insert_lower_bound(Node *t, const T &key, const T &val) { if(t) { splay(t); auto x = split_lower_bound(t, key); return merge(merge(x.first, alloc(key, val)), x.second); } else { return alloc(key, val); } } Node *update(Node *t) { t->sz = 1; t->sum = t->val; if(t->l) t->sz += t->l->sz, t->sum = max(t->sum, t->l->sum); if(t->r) t->sz += t->r->sz, t->sum = max(t->sum, t->r->sum); return t; } void propagate(Node *t, const T &x) { t->add += x; t->sum += x; t->val += x; } void push(Node *t) { if(t->add) { if(t->l) propagate(t->l, t->add); if(t->r) propagate(t->r, t->add); t->add = 0; } } private: void rotr(Node *t) { auto *x = t->p, *y = x->p; if((x->l = t->r)) t->r->p = x; t->r = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; update(y); } } void rotl(Node *t) { auto *x = t->p, *y = x->p; if((x->r = t->l)) t->l->p = x; t->l = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; update(y); } } Node *merge(Node *l) { return l; } }; int main() { int N; cin >> N; Graph<> g(N); for(int i = 1; i < N; i++) { int x; cin >> x; --x; g.add_directed_edge(x, i); } vector< int > A(N), B(N); cin >> A >> B; for(auto &a : A) --a; LazySplayTree< int64 > lst; vector< LazySplayTree< int64 >::Node * > dp(N); vector< pair< int64, int64 > > adds; auto dfs = MFP([&](auto dfs, int idx) -> void { int64 sum = 0; for(auto &to : g.g[idx]) { dfs(to); { auto[l, r] = lst.split_lower_bound(dp[to], A[idx]); if(r) sum += r->sum; dp[to] = lst.merge(l, r); } if(lst.count(dp[to]) > lst.count(dp[idx])) { swap(dp[to], dp[idx]); } int64 pre_key = -inf; while(lst.count(dp[to])) { dp[to] = lst.get_left(dp[to]); lst.splay(dp[to]); int64 key = dp[to]->key; int64 val = dp[to]->val; auto[l, buf] = lst.split_lower_bound(dp[idx], pre_key); auto[m, r] = lst.split_lower_bound(buf, dp[to]->key); if(m) lst.set_propagate(m, val); if(r) val += r->sum; dp[idx] = lst.merge(l, m, r); adds.emplace_back(key, val); pre_key = key; dp[to] = lst.erase(dp[to]); } for(auto&[key, val] : adds) { dp[idx] = lst.insert_lower_bound(dp[idx], key, val); } adds.clear(); } dp[idx] = lst.insert_lower_bound(dp[idx], A[idx], sum + B[idx]); }); dfs(0); cout << dp[0]->sum << "\n"; }