#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[8]={1,0,-1,0,1,1,-1,-1};
const ll dx[8]={0,1,0,-1,1,-1,1,-1};
template <typename T> inline bool chmax(T &a, T b) {
  return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
  return ((a > b) ? (a = b, true) : (false));
}
int main(){
  ll n;cin >> n;
  using ld=long double;
  vector<ld> a(n),b(n);
  rep(i,n)cin >> a[i];
  rep(i,n)cin >> b[i];
  vector<ld> minis(n);
  ld mx=inf;
  per(i,n){
    minis[i]=mx;
    chmin(mx,a[i]/b[i]);
  }
  ld ans=0;
  ld num=0,den=0;
  CST(10);
  rep(i,n){
    num+=a[i],den+=b[i];
    if(num/den<1){
      ans+=num+den;
      num=0;den=0;
    }
    else if(num/den<minis[i]){
      ans+=sqrtl(num*den)*2;
      num=0,den=0;
    }
  }
  cout << ans << endl;
}