#include<bits/stdc++.h>
using namespace std;
int main(){
  int n;
  cin>>n;
  vector<long long >a(n),b(n);
  for(int i=0;i<n;i++)cin>>a[i];
  for(int i=0;i<n;i++)cin>>b[i];
  vector<pair<long long,long long>>ret;
  for(int i=n-1;i>=0;i--){
    long long now_a=a[i],now_b=b[i];
    while(ret.size()&&!((double)ret.back().first/ret.back().second>=(double)now_a/now_b)){
      now_a+=ret.back().first;
      now_b+=ret.back().second;
      ret.pop_back();
    }
    ret.push_back({now_a,now_b});
  }
  double ans=0;
  for(auto&[x,y]:ret){
    if(x>=y)ans+=2.0*sqrt(x)*sqrt(y);
    else ans+=x+y;
  }
  cout<<fixed<<setprecision(10)<<ans<<endl;
}