#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

int main() {
  int n; cin >> n;
  vector<int> a(n), b(n);
  REP(i, n) cin >> a[i];
  REP(i, n) cin >> b[i];
  vector<ll> c, d;
  c.reserve(n);
  d.reserve(n);
  for (int i = n - 1; i >= 0; --i) {
    ll x = a[i], y = b[i];
    while (!c.empty() && __int128(x) * d.back() >= __int128(c.back()) * y) {
      x += c.back();
      y += d.back();
      c.pop_back();
      d.pop_back();
    }
    c.emplace_back(x);
    d.emplace_back(y);
  }
  n = c.size();
  double ans = 0;
  REP(i, n) ans += (c[i] < d[i] ? c[i] + d[i] : 2 * sqrt(static_cast<double>(c[i]) * d[i]));
  cout << ans << '\n';
  return 0;
}