#include <algorithm>
#include <array>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <queue>

using namespace std;

struct BoolName : numpunct<char> {
  string t, f;
  BoolName (string t = "Yes", string f = "No") : t(t), f(f) {}
  string do_truename() const {return t;}
  string do_falsename() const {return f;}
};

struct Initializer {
  Initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(15) << boolalpha;
    cout.imbue(locale(cout.getloc(), new BoolName));
  }
} initializer;

template<typename T> istream& operator>>(istream &s, vector<T> &v) {
  for (T &t : v) s >> t;
  return s;
}

template<typename T> ostream& operator<<(ostream &s, const vector<T> &v) {
  for (const T &t : v) s << t << endl;
  return s;
}

void set_bool_name(string t, string f) {
  cout.imbue(locale(cout.getloc(), new BoolName(t, f)));
}

template<typename T> bool chmin(T& a, T b) {return a > b ? a = b, true : false;}

template<typename T> bool chmax(T& a, T b) {return a < b ? a = b, true : false;}

template<typename T> void sort(vector<T>& v) {sort(v.begin(), v.end());}

template<typename T> int least_bit(T n) {
  static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size");
  if (sizeof(T) == 4) return __builtin_ffs(n) - 1;
  if (sizeof(T) == 8) return __builtin_ffsll(n) - 1;
}

// n must be greater than 0.
template<typename T> int least_bit_fast(T n) {
  static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size");
  if (sizeof(T) == 4) return __builtin_ctz(n);
  if (sizeof(T) == 8) return __builtin_ctzll(n);
}

template<typename T> int most_bit(T n) {
  static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size");
  if (sizeof(T) == 4) return n ? 31 - __builtin_clz(n) : -1;
  if (sizeof(T) == 8) return n ? 63 - __builtin_clzll(n) : -1;
}

template<typename T> int count_bit(T n) {
  static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size");
  if (sizeof(T) == 4) return __builtin_popcount(n);
  if (sizeof(T) == 8) return __builtin_popcountll(n);
}

template<typename T = double> constexpr T pi() {return acos(T(-1));}

template<typename T> T gcd(T t) {return abs(t);}

template<typename T, typename... S> T gcd(T a, S... s) {
  a = abs(a);
  auto b = gcd(s...);
  if (a == 0 || b == 0) return max(a, b);
  int fa = least_bit_fast(a);
  int fb = least_bit_fast(b);
  a >>= fa;
  b >>= fb;
  while (a != b) {
    auto& c = a > b ? a : b;
    c = abs(a - b);
    c >>= least_bit_fast(c);
  }
  return a << min(fa, fb);
}

template<typename T> T gcd(const vector<T>& v) {
  T g = abs(v[0]);
  for (int i = 1; i < int(v.size()); ++i) g = gcd(g, v[i]);
  return g;
}

template<typename T> T lcm(T t) {return abs(t);}

template<typename T, typename... S> T lcm(T t, S... s) {
  T l = lcm(s...);
  return abs(t) / gcd(t, l) * l;
}

template<typename T> T lcm(const vector<T>& v) {
  T l = abs(v[0]);
  for (int i = 1; i < int(v.size()); ++i) l = lcm(l, v[i]);
  return l;
}

template<typename T> T floor(T a, T b) {
  auto d = div(a, b);
  return d.quot - (d.rem && (a < 0) != (b < 0) ? 1 : 0);
}

template<typename T> T ceil(T a, T b) {
  auto d = div(a, b);
  return d.quot + (d.rem && (a > 0) == (b > 0) ? 1 : 0);
}

template<typename T> T round(T a, T b) {return floor(a + b / 2, b);}

template<typename T> T mod(T a, T b) {
  T c = a % b;
  return c < 0 ? c + abs(b) : c;
}

template<typename T> T factorial(T n) {return n <= 1 ? 1 : factorial(n - 1) * n;}

template<typename T> vector<T> factorial_vector(int n) {
  vector<T> v(n + 1, 1);
  for (int i = 1; i <= n; ++i) v[i] = v[i - 1] * i;
  return v;
}

template<typename T> T square(T n) {return n * n;}

template<typename T> T cube(T n) {return n * n * n;}

template<typename T> T norm(T x1, T y1, T x2, T y2) {return square(x1 - x2) + square(y1 - y2);}

template<typename T> bool isSquare(T n) {return square(T(sqrt(n))) == n;}

template<typename T> T clamp(T v, T l, T u) {return v < l ? l : v > u ? u : v;}

int main() {
  int n;
  cin >> n;
  vector<double> t(n), v(n);
  cin >> t >> v;
  constexpr double INF = numeric_limits<double>::max();
  vector<vector<double>> dp(n + 1, vector<double>(101, INF));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j <= v[i]; ++j) {
      if (dp[i][j] == INF) continue;
      for (int k = 0; k <= v[i]; ++k) {
        if (t[i] < abs(j - k)) continue;
        double vm = min(v[i], (j + k) / 2.0 + t[i] / 2.0);
        dp[i + 1][k] = dp[i][j] + t[i] * vm - square(vm - j) / 2.0 - square(vm - k) / 2.0;
      }
    }
  }
  cout << dp[n][0] << endl;
}



Measured memory_bytes: 384