#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic pop
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  VI a(n), b(n);
  rep(i, n) cin >> a[i];
  rep(i, n) cin >> b[i];
  double ans = 0;
  double lb = 1.0;
  for(int i = 0; i < n;) {
    double sa = a[i];
    double sb = b[i];
    double x = max(lb, sqrt(sa / sb));
    int j = i + 1;
    while(j < n) {
      double nx = max(lb, sqrt((sa + a[j]) / (sb + b[j])));
      if (x < nx) break;
      sa += a[j];
      sb += b[j];
      x = nx;
      j++;
    }
    ans += sa / x + sb * x;
    lb = x;
    i = j;
  }
  cout << fixed << setprecision(12) << ans << '\n';
}