#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i = 0; i < (int)n; i++)
#define FOR(n) for(int i = 0; i < (int)n; i++)
#define repi(i,a,b) for(int i = (int)a; i < (int)b; i++)
#define pb push_back
#define m0(x) memset(x,0,sizeof(x))
#define fill(x,y) memset(x,y,sizeof(x))
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
//#define mp make_pair
#define vi vector<int>
#define vvi vector<vi>
#define vll vector<ll>
#define vvll vector<vll>
#define vs vector<string>
#define vvs vector<vs>
#define vc vector<char>
#define vvc vector<vc>
#define pii pair<int,int>
#define pllll pair<ll,ll>
#define vpii vector<pair<int,int>>
#define vpllll vector<pair<ll,ll>>
#define vpis vector<pair<int,string>>
#define vplls vector<pair<ll, string>>
#define vpsi vector<pair<string, int>>
#define vpsll vector<pair<string, ll>>

template<typename T>
void chmax(T &a, const T &b) {a = (a > b? a : b);}
template<typename T>
void chmin(T &a, const T &b) {a = (a < b? a : b);}

using ll = long long;
using ld = long double;
using ull = unsigned long long;

const ll INF = numeric_limits<long long>::max() / 2;
const ld pi = 3.1415926535897932384626433832795028;
const ll mod = 1e9 + 7;
int dx[] = {-1, 0, 1, 0, -1, -1, 1, 1};
int dy[] = {0, -1, 0, 1, -1, 1, -1, 1};

#define int long long

void solve() {
    cout << fixed << setprecision(10);

    int n;
    cin >> n;
    vector<ld> a(n), b(n);
    FOR(n) cin >> a[i];
    FOR(n) cin >> b[i];
    vector<ld> tota(n+1), totb(n+1);
    FOR(n) {
        tota[i+1] = tota[i] + a[i];
        totb[i+1] = totb[i] + b[i];
    }

    ld ans = 0;
    ld x = 0;
    FOR(n) {
        if(a[i] <= b[i]) {
            ans += a[i]/(1+x)+b[i]*(1+x);;
            continue;
        }
        ld ad = tota[n]-tota[i];
        ld bd = totb[n]-totb[i];
        ld candidate = min(-1+sqrt(ad/bd), sqrt(a[i]/b[i]-1));
        chmax(x, candidate);

        ans += a[i]/(1+x)+b[i]*(1+x);

        // cout << ad << " " << bd << " " << candidate << endl;
    }

    cout << ans << endl;
}

signed main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    solve();
    return 0;
}