#include <bits/stdc++.h>
#include<complex>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vvvvll = vector<vvvll>;
using vvvvvll = vector<vvvvll>;
#define all(A) A.begin(),A.end()
#define rep(i, n) for (ll i = 0; i < (ll) (n); i++)
template<class T>
bool chmax(T& p, T q, bool C = 1) {
    if (C == 0 && p == q) {
        return 1;
    }
    if (p < q) {
        p = q;
        return 1;
    }
    else {
        return 0;
    }
}

template<class T>
bool chmin(T& p, T q, bool C = 1) {
    if (C == 0 && p == q) {
        return 1;
    }
    if (p > q) {
        p = q;
        return 1;
    }
    else {
        return 0;
    }
}

ll gcd(ll(a), ll(b)) {
    if (a == 0)return b;
    if (b == 0)return a;
    ll c = a;
    while (a % b != 0) {
        c = a % b;
        a = b;
        b = c;
    }
    return b;
}
ll sqrtz(ll N) {
    ll L = 0;
    ll R = sqrt(N) + 10000;
    while (abs(R - L) > 1) {
        ll mid = (R + L) / 2;
        if (mid * mid <= N)L = mid;
        else R = mid;
    }
    return L;

}
ll modPow(long long a, long long n, long long p) {
    if (n == 0) return 1; // 0乗にも対応する場合
    if (n == 1) return a % p;
    if (n % 2 == 1) return (a * modPow(a, n - 1, p)) % p;
    long long t = modPow(a, n / 2, p);
    return (t * t) % p;
}

using mint = modint;
using vm = vector<mint>;
using vvm = vector<vm>;
using vvvm = vector<vvm>;


vector<mint> fact, factinv, inv, factK;
ll mod = 1000000007;
void prenCkModp(ll n) {
    // factK.resize(4*n+5);
    fact.resize(n + 5);
    factinv.resize(n + 5);
    inv.resize(n + 5);
    fact[0] = fact[1] = 1;
    factinv[0] = factinv[1] = 1;
    inv[1] = 1;
    for (ll i = 2; i < n + 5; i++) {
        fact[i] = (fact[i - 1] * i);
        inv[i] = (mod - ((inv[mod % i] * (mod / i))));
        factinv[i] = (factinv[i - 1] * inv[i]);
    }
    // factK[0]=1;
    // for(ll i=1;i<4*n+5;i++){
    //    factK[i]=factK[i-1]*mint(K-i+1);
    //    //K*(K-1)*...*(K-i+1);
    // }
}
mint nCk(ll n, ll k) {
    if (n < k || k < 0) return 0;
    return (fact[n] * ((factinv[k] * factinv[n - k])));
}
// ll K;
// mint nCkK(ll n,ll k){
//    if(K<n||K-n<k)return 0;
//    mint res=factK[n+k];
//    res*=factK[n].inv();
//    res*=factinv[k];
//    return res;
// }


int main() {

    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    ll N;
    cin>>N;
    vll A(N);
    vll B(N);
    rep(i,N)cin>>A[i];
    rep(i,N)cin>>B[i];
    stack<pair<ll,ll>> P;
    rep(i,N){
        P.push({B[i],A[i]});
        while(P.size()>1){
            ll p=P.top().first;
            ll q=P.top().second;
            P.pop();
            ll b=P.top().first;
            ll a=P.top().second;
            if(a*p>=b*q){
                P.pop();
                b+=p;
                a+=q;
                P.push({b,a});
            }
            else{
                P.push({p,q});
                break;
            }
        }
    }
    double an=0.0;
    vector<double> Q,R;
    while(!P.size()==0){
        R.push_back(double(P.top().first));
        Q.push_back(double(P.top().second));
        P.pop();
    }
    reverse(all(Q));
    reverse(all(R));
    N=Q.size();
    double x=0;
    rep(i,N){
        if(Q[i]/R[i]<=1.0){

        }
        else{
            x=sqrt(Q[i]/R[i])-1.0;
        }
        an+=(Q[i]/(1.0+x))+(R[i]*(1.0+x));
    }
    cout<<fixed<<setprecision(15);
    cout<<an<<endl;


}