#ifndef DEBUG
#  define NDEBUG
#endif
#include <iostream>
#include <iomanip>
#include <string>
#include <iterator>
#include <utility>
#include <type_traits>
#include <limits>
#include <cassert>
#include <vector>
#include <numeric>
#include <set>

using namespace std;

// template {{{
// misc {{{
using Z = int;
[[maybe_unused]]
constexpr Z INF = numeric_limits<Z>::max() / 3;
// }}}

// debug {{{
template <class T>
using enable_if_sequence_t = enable_if_t<
  is_same<
    typename iterator_traits<
      typename remove_cv_t<remove_reference_t<T>>::iterator
    >::iterator_category,
    random_access_iterator_tag>{}>;
#ifdef NDEBUG
# define dump(x)
# define debug if (0)
template <class T>
inline T&& ix(T&& value) { return value; }
template <class T, class Index, class... Indices, class = enable_if_sequence_t<T>>
inline auto&& ix(T&& container, Index index, Indices... indices) {
  return ix(container[index], indices...);
}
#else
# define dump(x) do { \
    cerr << "\e[33m[dump: " << __LINE__ << "] " << (#x) << " = " << x << "\e[0m" << endl; \
  } while (0);
# define debug
template <class T>
inline auto&& ix_impl([[maybe_unused]] int line, [[maybe_unused]] const char* code, T&& value) {
  return value;
}
template <class T, class Index, class... Indices, class = enable_if_sequence_t<T>>
inline auto&& ix_impl(int line, const char* code, T&& container, Index index, Indices... indices) {
  if (index < 0) {
    cerr << "\e[31mix: negative index at line " << line << ", ix(" << code << ")\e[0m" << endl;
    exit(1);
  }
  int size = container.size();
  if (index >= size) {
    cerr << "\e[31mix: index out of range at line " << line << ", ix(" << code << ")\n"
      << "index = " << index << " whereas size = " << size << "\e[0m" << endl;
    exit(1);
  }
  return ix_impl(line, code, container[index], indices...);
}
#define ix(...) ix_impl(__LINE__, #__VA_ARGS__, __VA_ARGS__)
#endif
// }}}

// IO {{{
template <class T>
false_type is_container_impl(...);
template <class T, class = typename T::iterator>
true_type is_container_impl(T);
template <class T>
struct is_container : decltype(is_container_impl<T>(declval<T>())) {};
template <>
struct is_container <string> : std::false_type {};
template <class Container, class = enable_if_t<is_container<Container>{}>>
istream& operator>> (istream& is, Container& cont) {
  for (auto& v : cont) is >> v;
  return is;
}
template <class Container, class = enable_if_t<is_container<Container>{}>>
ostream& operator<< (ostream& os, Container const& cont) {
  bool first = true;
  constexpr char sep =
    is_container<typename Container::value_type>{} ? '\n' : ' ';
  for (auto const& v : cont) {
    if (!first) {
      os << sep;
    }
    first = false;
    os << v;
  }
  return os;
}
template <class T, class U>
ostream& operator<< (ostream& os, pair<T, U> p) {
  os << '(' << p.first << ", " << p.second << ')';
  return os;
}
// }}}
// }}}

struct line_segment {
  Z left, right, slant, ly;

  template <class T>
  T y_at(T x) const {
    assert(T(left) <= x && x <= T(right));
    return (x - T(left)) * T(slant) + T(ly);
  }

  pair<double, double> intersection(line_segment const& l) {
    Z common_l = max(left, l.left),
      common_r = min(right, l.right);
    if (common_l > common_r)
      return {-1, -1};
    Z tl = y_at(common_l), tr = y_at(common_r),
      ll = l.y_at(common_l), lr = l.y_at(common_r);
    if ((tl > ll && tr > lr) || (tl < ll && tr < lr))
      return {-1, -1};
    if (common_l == common_r)
      return {common_l, y_at(common_l)};
    double ldiff = abs(tl - ll), rdiff = abs(tr - lr);
    // well, well...
    if (ldiff == 0 && rdiff == 0)
      return {-10, -10};
    double x = (double(common_l) * rdiff + double(common_r) * ldiff) / (ldiff + rdiff);
    return {x, y_at(x)};
  }
};

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  Z N;
  cin >> N;
  vector<Z> t(N), v(N);
  cin >> t >> v;
  vector<line_segment> restrictions;
  Z duration = 0, total_duration = accumulate(begin(t), end(t), 0);
  restrictions.push_back({0, total_duration, 1, 0});
  restrictions.push_back({0, total_duration, -1, total_duration});
  for (auto i = 0; i < N; i++) {
    if (i != 0)
      restrictions.push_back({0, duration, -1, v[i] + duration});
    restrictions.push_back({duration, duration + t[i], 0, v[i]});
    if (i != N - 1)
      restrictions.push_back({duration + t[i], total_duration, 1, v[i]});
    duration += t[i];
  }
  debug {
    for (auto&& e : restrictions) {
      dump(e.left);
      dump(e.right);
      dump(e.slant);
      dump(e.ly);
    }
    cerr << "-----------" << endl;
  }
  vector<line_segment> refined;
  for (auto&& e : restrictions) {
    bool merged = false;
    for (auto&& r : refined) {
      auto p = e.intersection(r);
      if (p.first != -10) continue;
      if (e.left < r.left) {
        r.left = e.left;
        r.ly = e.ly;
      }
      if (e.right > r.right)
        r.right = e.right;
      merged = true;
    }
    if (!merged) refined.push_back(e);
  }
  set<double> intersections;
  for (auto&& a : refined) {
    for (auto&& b : refined) {
      auto p = a.intersection(b);
      if (p.first < 0) continue;
      intersections.insert(p.first);
    }
  }
  intersections.insert(0);
  intersections.insert(total_duration);
  double dist = 0;
  for (auto it = begin(intersections); next(it) != end(intersections); ++it) {
    double left = *it, right = *next(it),
           min_l = 1000, min_r = 1000;
    dump(left); dump(right);
    for (auto&& e : refined) {
      if (left < e.left || e.right < right)
        continue;
      dump(e.left); dump(e.right);
      min_l = min(min_l, e.y_at(left));
      min_r = min(min_r, e.y_at(right));
    }
    dist += (right - left) * (min_l + min_r) / 2;
  }
  cout << setprecision(10) << dist << endl;
}



Measured memory_bytes: 512