#include <bits/stdc++.h>
using namespace std;
const char el = '\n';
typedef long long ll;
typedef long double ld;
int n;
vector<ll> p, q;
pair<ld, ld> prob(int p, int q) {
  int a, b, c;
  if (p <= q)
    a = p * (p + 1) / 2, b = p, c = p * (q + 1) - b - a;
  else
    c = (q - 1) * q / 2, b = q, a = p * (q + 1) - b - c;
  return {1.0 * a / (a + b + c), 1.0 * c / (a + b + c)};
}
const int maxn = 1e6 + 5;
ld solve1(int k);
ld solve3(int k) {
  static vector<ld> mem(maxn, -1);
  if (k == n) return 1;
  ld &res = mem[k];
  if (res > -0.5) return res;
  res = 0;
  for (int i = 1; i <= p[k] && k + i <= n; i++) {
    res = max(res, 1-solve1(k + i));
  }
  return res;
}
ld solve2(int k) {
  static vector<ld> mem(maxn, -1);
  if (k == n) return 1;
  ld &res = mem[k];
  if (res > -0.5) return res;
  res = 0;
  for (int i = 1; i <= p[k] && k + i <= n; i++) {
    res = max(res, solve1(k + i));
  }
  return res;
}
ld solve1(int k) {
  static vector<ld> mem(maxn, -1);
  if (k == n) return 0;
  ld &res = mem[k];
  if (res > -0.5) return res;
  res = 0;
  for (int i = 1; i <= p[k] && k + i <= n; i++) {
    res = max(res, 1 - solve1(k + i));
    if (p[k] == i || k + i == n) continue;
    auto [x, y] = prob(p[k] - i, q[k] + q[k + i]);
    res = max(res, x * solve3(k + i) + (1 - x - y) * (1 - solve1(k + i)) +
                       y * (1 - solve2(k + i)));
  }
  return res;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(15);
  cin >> n;
  p.resize(n), q.resize(n);
  for (auto &v : p) cin >> v;
  for (auto &v : q) cin >> v;
  cout << solve1(0) << el;
  return 0;
}