#include <bits/stdc++.h>
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-const-variable"
using namespace std;
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  static Type inverse(Type a, Type mod) {
    Type b = mod, x = 0, y = 1;
    while (a != 0) {
      Type t = b / a;
      b -= a * t;
      x -= t * y;
      swap(a, b);
      swap(x, y);
    }
    if (x < 0) x += mod;
    return x;
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  template <typename U>
  friend const Modular<U>& abs(const Modular<U>& v) {
    return v;
  }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
const int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
long long sqr(long long x) { return x * x; }
int mysqrt(long long x) {
  int l = 0, r = 1e9 + 1;
  while (r - l > 1) {
    int m = (l + r) / 2;
    if (m * (long long)m <= x)
      l = m;
    else
      r = m;
  }
  return l;
}
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rndll(
    chrono::high_resolution_clock::now().time_since_epoch().count());
template <typename T>
T gcd(T a, T b) {
  return a ? gcd(b % a, a) : b;
}
int gcdex(int a, int b, int& x, int& y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  int x1, y1;
  int ret = gcdex(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return ret;
}
void setmin(int& x, int y) { x = min(x, y); }
void setmax(int& x, int y) { x = max(x, y); }
void setmin(long long& x, long long y) { x = min(x, y); }
void setmax(long long& x, long long y) { x = max(x, y); }
const long long llinf = 4e18 + 100;
const long double eps = 1e-9, PI = atan2(0, -1);
const int maxn = 2e5 + 100, maxw = 1e4 + 100, inf = 1e9 + 100, sq = 450,
          LG = 18, mod = 1e9 + 933;
int tp[maxn], h[maxn], n;
vector<int> e[maxn];
long long q[maxn][2];
void dfs(int v, int par) {
  int X = 0, Y = 0;
  vector<long long> g;
  long long cur = 0;
  for (int i : e[v])
    if (i != par) {
      dfs(i, v);
      if (h[i] == h[v]) {
        g.push_back(q[i][1] - q[i][0]);
        cur += q[i][0];
        X++;
      } else if (h[i] < h[v]) {
        X++;
        cur += q[i][0];
      } else {
        Y++;
        cur += q[i][1];
      }
    }
  sort(g.begin(), g.end());
  q[v][0] = q[v][1] = llinf;
  auto upd = [&](int t, int x, int y) {
    setmin(q[v][t], max(x, y) * (long long)tp[v] + cur);
  };
  for (int i = 0; i <= g.size(); i++) {
    if (par == -1)
      upd(0, X, Y);
    else {
      upd(0, X, Y + 1);
      upd(1, X + 1, Y);
    }
    if (i < g.size()) {
      cur += g[i];
      X--;
      Y++;
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> tp[i];
  for (int i = 0; i < n; i++) cin >> h[i];
  for (int i = 1; i < n; i++) {
    int v, u;
    cin >> v >> u;
    v--;
    u--;
    e[v].push_back(u);
    e[u].push_back(v);
  }
  dfs(0, -1);
  cout << q[0][0] << '\n';
}
