#include "bits/stdc++.h"
#ifndef err
#define err(...)(void)0
#endif
using namespace std;
using ll = long long;
using ull = decltype(1ull);
template<class T>int size(T&&a) { return a.size(); }
#define REP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.first,_l##t=a.second;t<_l##t;t++)
#define RREP(t,a)for(typename make_signed<decltype(a.second)>::type t=a.second-1,_l##t=a.first;t>=_l##t;t--)
template<class B>pair<int, B>make_pair(B b) { return{ 0,b }; }
#define rep(t,...)REP(t,make_pair(__VA_ARGS__))
#define rrep(t,...)RREP(t,make_pair(__VA_ARGS__))
#define all(a)begin(a),end(a)
#define rall(a)a.rbegin(),a.rend()
#define var(t, ...) t __VA_ARGS__;in,__VA_ARGS__;

void Calc();
int main() {
  ios::sync_with_stdio(false); cin.tie(nullptr);
  cin.exceptions(istream::failbit | istream::badbit);
  cout << fixed << setprecision(15); Calc(); cout.flush(); return 0;
}
template<class A>void amax(A&a, A b) { a = max(a, b); }
template<class A>void amin(A&a, A b) { a = min(a, b); }
template<class A>int comp(A a, A b) { return a < b ? 1 : b < a ? -1 : 0; }
struct Scanner {
  template<class A = string>A Next() { A a; cin >> a; return a; }
  template<class A = int>vector<A>Array(int n) { vector<A>a(n); for (A&i : a) cin >> i; return a; }
  string Line() const { string s; getline(cin, s); return s; }
  template<class A>Scanner&operator,(A&a) { a = Next<A>(); return *this; }
  template<class A>operator A() { return Next<A>(); }
}in;

/*---------------------------------------------------------------------*/

template<class ...T>tuple<T...>Init(T... t) { return tuple<T...>{ t... }; }
template<class T>tuple<T> Init(T t) { return tuple<T>{ t }; }
template<int N, int...I>struct idx_seq : idx_seq<N - 1, 0, (I + 1)...> {};
template<int...I>struct idx_seq<0, I...> {};
template<class R, class T, int...I>R InitInternal(T&&a, idx_seq<0, I...>) { return R{ get<I>(a)... }; }
template<class T, class B, class...V>struct Vec {
  typedef Vec<T, V...>A; typedef vector<typename A::t>t; t nvec(B a, V...b) { return t(a, A().nvec(b...)); }
};
template<class T, class B>struct Vec<T, B> {
  using X = typename conditional<is_same<T, nullptr_t>::value, int, T>::type;
  typedef vector<X>t; t nvec(B a) { return t(a); }
};
template<class T, class ...C>struct Vec<T, tuple<C...>> {
  template<class A, class B>static pair<A, B> X(A, B);
  template<class...A>static tuple<A...> X(A...);
  using t = typename conditional < is_same<T, nullptr_t>::value, decltype(X(C{}...)), T > ::type;
  t nvec(tuple<C...> a) { return InitInternal<t>(a, idx_seq<sizeof...(C)>()); }
};
template<class T, class C>struct Vec<T, tuple<C>> {
  using X = typename conditional<is_same<T, nullptr_t>::value, C, T>::type;
  using t = X; t nvec(tuple<C> a) { return { get<0>(a) }; }
};
template<class T = nullptr_t, class...B> typename Vec<T, B...>::t nvec(B...b) { return Vec<T, B...>().nvec(b...); }



void Calc() {

  int n = in;
  auto t = in.Array(n);
  auto v = in.Array(n);


  auto dp = nvec<double>(n + 1, 101, Init(-1.0));
  dp[0][0] = 0;
  auto f = [&](int i, int vp, int vn) {
    if (abs(vp - vn) > t[i]) return -1.0;
    if (vn > v[i])return -1.0;
    if (vp > v[i])return -1.0;

    double l = (t[i] + (vn - vp)) / 2.0;
    double ans = 0;
    if (l + vp > v[i]) {
      l = v[i] - vp;
      int r = max(0, v[i] - vn);
      ans += l * l / 2.0 + vp * l;
      double mid = max(0.0, t[i] - l - r);
      ans += mid * (l + vp);
      ans += r*r / 2. + vn * r;
      return ans;
    }
    ans += l * l / 2 + vp * l;
    double r = max(0., l - (vn - vp));
    ans += r*r / 2 + r * vn;
    return ans;
  };
  rep(i, n)rep(j, 101)if (dp[i][j] >= 0) {
    rep(k, 101) {
      auto c = f(i, j, k);
      if (c >= 0)
        amax(dp[i + 1][k], dp[i][j] + c);
    }
  }
  cout << (dp[n][0]) << endl;
}


Measured memory_bytes: 384