Igor is a post-graduate student of chemistry faculty in Berland State University (BerSU). He needs to conduct a complicated experiment to write his thesis, but laboratory of BerSU doesn't contain all the materials required for this experiment.

Fortunately, chemical laws allow material transformations (yes, chemistry in Berland differs from ours). But the rules of transformation are a bit strange.

Berland chemists are aware of n materials, numbered in the order they were discovered. Each material can be transformed into some other material (or vice versa). Formally, for each i (2 ≤ i ≤ n) there exist two numbers xi and ki that denote a possible transformation: ki kilograms of material xi can be transformed into 1 kilogram of material i, and 1 kilogram of material i can be transformed into 1 kilogram of material xi. Chemical processing equipment in BerSU allows only such transformation that the amount of resulting material is always an integer number of kilograms.

For each i (1 ≤ i ≤ n) Igor knows that the experiment requires ai kilograms of material i, and the laboratory contains bi kilograms of this material. Is it possible to conduct an experiment after transforming some materials (or none)?

Input

The first line contains one integer number n (1 ≤ n ≤ 105) — the number of materials discovered by Berland chemists.

The second line contains n integer numbers b1, b2... bn (1 ≤ bi ≤ 1012) — supplies of BerSU laboratory.

The third line contains n integer numbers a1, a2... an (1 ≤ ai ≤ 1012) — the amounts required for the experiment.

Then n - 1 lines follow. j-th of them contains two numbers xj + 1 and kj + 1 that denote transformation of (j + 1)-th material (1 ≤ xj + 1 ≤ j, 1 ≤ kj + 1 ≤ 109).

Output

Print YES if it is possible to conduct an experiment. Otherwise print NO.

Examples

Input

3
1 2 3
3 2 1
1 1
1 1


Output

YES


Input

3
3 2 1
1 2 3
1 1
1 2


Output

NO
#include <bits/stdc++.h>
using namespace std;
template <typename... As>
struct tpl : public std::tuple<As...> {
  using std::tuple<As...>::tuple;
  tpl() {}
  tpl(std::tuple<As...> const& b) { std::tuple<As...>::operator=(b); }
  template <typename T = tuple<As...>>
  typename tuple_element<0, T>::type const& x() const {
    return get<0>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<0, T>::type& x() {
    return get<0>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<1, T>::type const& y() const {
    return get<1>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<1, T>::type& y() {
    return get<1>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<2, T>::type const& z() const {
    return get<2>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<2, T>::type& z() {
    return get<2>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<3, T>::type const& w() const {
    return get<3>(*this);
  }
  template <typename T = tuple<As...>>
  typename tuple_element<3, T>::type& w() {
    return get<3>(*this);
  }
};
using lli = long long int;
using llu = long long unsigned;
using pii = tpl<lli, lli>;
using piii = tpl<lli, lli, lli>;
using piiii = tpl<lli, lli, lli, lli>;
using vi = vector<lli>;
using vii = vector<pii>;
using viii = vector<piii>;
using vvi = vector<vi>;
using vvii = vector<vii>;
using vviii = vector<viii>;
template <class T>
using min_queue = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using max_queue = priority_queue<T>;
template <size_t... I>
struct my_index_sequence {
  using type = my_index_sequence;
  static constexpr array<size_t, sizeof...(I)> value = {{I...}};
};
namespace my_index_sequence_detail {
template <typename I, typename J>
struct concat;
template <size_t... I, size_t... J>
struct concat<my_index_sequence<I...>, my_index_sequence<J...>>
    : my_index_sequence<I..., (sizeof...(I) + J)...> {};
template <size_t N>
struct make_index_sequence
    : concat<typename make_index_sequence<N / 2>::type,
             typename make_index_sequence<N - N / 2>::type>::type {};
template <>
struct make_index_sequence<0> : my_index_sequence<> {};
template <>
struct make_index_sequence<1> : my_index_sequence<0> {};
}  // namespace my_index_sequence_detail
template <class... A>
using my_index_sequence_for =
    typename my_index_sequence_detail::make_index_sequence<sizeof...(A)>::type;
template <class T, size_t... I>
void print_tuple(ostream& s, T const& a, my_index_sequence<I...>) {
  using swallow = int[];
  (void)swallow{0, (void(s << (I == 0 ? "" : ", ") << get<I>(a)), 0)...};
}
template <class T>
ostream& print_collection(ostream& s, T const& a);
template <class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a);
template <class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a);
template <class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a);
template <class T, size_t I>
ostream& operator<<(ostream& s, array<T, I> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, vector<T> const& a) {
  return print_collection(s, a);
}
template <class T, class U>
ostream& operator<<(ostream& s, multimap<T, U> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, multiset<T> const& a) {
  return print_collection(s, a);
}
template <class T, class U>
ostream& operator<<(ostream& s, map<T, U> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& operator<<(ostream& s, set<T> const& a) {
  return print_collection(s, a);
}
template <class T>
ostream& print_collection(ostream& s, T const& a) {
  s << '[';
  for (auto it = begin(a); it != end(a); ++it) {
    s << *it;
    if (it != prev(end(a))) s << " ";
  }
  return s << ']';
}
template <class... A>
ostream& operator<<(ostream& s, tpl<A...> const& a) {
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}
template <class... A>
ostream& operator<<(ostream& s, tuple<A...> const& a) {
  s << '(';
  print_tuple(s, a, my_index_sequence_for<A...>{});
  return s << ')';
}
template <class A, class B>
ostream& operator<<(ostream& s, pair<A, B> const& a) {
  return s << "(" << get<0>(a) << ", " << get<1>(a) << ")";
}
namespace std {
namespace {
template <class T>
inline void hash_combine(size_t& seed, T const& v) {
  seed ^= hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
template <class Tuple, size_t Index = tuple_size<Tuple>::value - 1>
struct HashValueImpl {
  static void apply(size_t& seed, Tuple const& tuple) {
    HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
    hash_combine(seed, get<Index>(tuple));
  }
};
template <class Tuple>
struct HashValueImpl<Tuple, 0> {
  static void apply(size_t& seed, Tuple const& tuple) {
    hash_combine(seed, get<0>(tuple));
  }
};
}  // namespace
template <typename... TT>
struct hash<tuple<TT...>> {
  size_t operator()(tuple<TT...> const& tt) const {
    size_t seed = 0;
    HashValueImpl<tuple<TT...>>::apply(seed, tt);
    return seed;
  }
};
template <typename... TT>
struct hash<tpl<TT...>> {
  size_t operator()(tpl<TT...> const& tt) const {
    size_t seed = 0;
    HashValueImpl<tuple<TT...>>::apply(seed, tt);
    return seed;
  }
};
}  // namespace std
const int N = 1e5 + 16;
lli B[N];
lli A[N];
lli x[N];
lli k[N];
lli l10(lli x) {
  lli i = 0;
  x /= 10;
  while (x) {
    i += 1;
    x /= 10;
  }
  return i;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  lli n;
  cin >> n;
  for (lli i = 0; i < (lli)(n); ++i) cin >> B[i];
  for (lli i = 0; i < (lli)(n); ++i) cin >> A[i];
  vvi G(n);
  x[0] = -1;
  for (lli i = 0; i < (lli)(n - 1); ++i) {
    cin >> x[i + 1] >> k[i + 1];
    --x[i + 1];
    G[x[i + 1]].push_back(i + 1);
  }
  function<lli(lli)> dfs = [&](lli i) {
    lli self = B[i] - A[i];
    for (lli j : G[i]) {
      lli r = dfs(j);
      if (r >= 0)
        self += r;
      else {
        if (l10(k[j]) + l10(r - 1) >= 16) {
          self = -1e16;
        } else {
          self += k[j] * r;
        }
      }
    }
    return self;
  };
  lli ans = dfs(0);
  if (ans >= 0) {
    cout << "YES" << endl;
  } else {
    cout << "NO" << endl;
  }
  return 0;
}
