#include<iostream>
#include<vector>
#include<algorithm>
#include<cmath>
#include<string>
#include<iomanip>
#include<numeric>
#include<queue>
#include<stack>
#include<set>
#include<map>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
int dx[]={1,0,0,-1},dy[]={0,1,-1,0};
struct str{
	double tmp,a,b;
};
int main(){
	static int n,a[200000],b[200000];
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	for(int i=0;i<n;i++)
		cin>>b[i];
	static double ab[200000];
	for(int i=0;i<n;i++)
		ab[i]=sqrt((double)a[i]/b[i])-1;
	vector<str>vec;
	vec.push_back({0,0,0});
	for(int i=0;i<n;i++){
		str st{ab[i],a[i],b[i]};
		while(vec.size()&&vec.back().tmp>st.tmp){
			if(vec.back().tmp==0){
				st.tmp=0;
				break;
			}
			st.a+=vec.back().a;
			st.b+=vec.back().b;
			st.tmp=sqrt(st.a/st.b)-1;
			vec.pop_back();
		}
		vec.push_back(st);
	}
	double ans=0;
	for(auto x:vec)
		ans+=x.a/(1+x.tmp)+x.b*(1+x.tmp);
	cout<<fixed<<setprecision(20)<<ans<<endl;
}