#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
typedef int64_t lint;
#define rep(i, n) for(int i=0; i<n; i++)
#define repx(i, l, n) for(int i=l; i<n; i++)
#define all(v) v.begin(), v.end()
#define show(x) cout << #x << ": " << x << endl;
#define list(x) cout << #x << ": " << x << "  ";
#define pb push_back
using vi = vector<lint>;
using vvi = vector<vector<lint>>;
template<class T> inline void vin(vector<T>& v) { rep(i, v.size()) cin >> v.at(i); }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<class T> inline void drop(T x) { cout << x << endl; exit(0); }
template<class T> void vout(vector<T> v) { rep(i, v.size()) { cout << v.at(i) << ' '; } cout << endl; }
constexpr lint LINF = LLONG_MAX/2;
using pint = pair<lint, lint>;
using vp = vector<pint>;

int main() {
	lint N;
	cin >> N;
	vi v(N), w(N);
	vin(v);
	vin(w);

	long double a=0, b=0, c=0, x=0, y=0, z;
	stack<pint> s;
	rep(i, N) {
		x = v[N-1-i], y = w[N-1-i];
		while (!s.empty()) {
			tie(b, c) = s.top();
			if (x*c >= b*y) {
				s.pop();
				x += b, y += c;
			} else {
				break;
			}
		}
		s.push({x, y});
	}
	while (!s.empty()) {
		tie(x, y) = s.top();
		s.pop();
		if (x < y) a += x+y;
		else {
			z = sqrt((double)x/y);
			a += x/z+y*z;
		}
	}
	cout << fixed << setprecision(10) << a << endl;
}