#include <bits/stdc++.h>
//#include <atcoder/all>
using namespace std;
//using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
//using mint = modint998244353;
//const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define endl "\n"
#define P pair<double,double>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int n; cin >> n;
	vector<double>a(n), b(n);
	rep(i, n)cin >> a[i];
	rep(i, n)cin >> b[i];
	double ans = 0;
	stack<P>st;
	rrep(i, n) {
		double x = a[i];
		double y = b[i];
		while (!st.empty()) {
			auto[x1, y1] = st.top();
			if (x* y1 >= x1 * y) {
				st.pop();
				x += x1;
				y += y1;
			}
			else break;
		}
		st.push({ x,y });
	}
	while (!st.empty()) {
		auto[x, y] = st.top();
		st.pop();
		if (x < y) ans += x + y;
		else {
			double z = sqrt(x / y);
			ans += x / z + y * z;
		}
	}
	printf("%.16f\n", ans);
	return 0;
}