#include <bits/stdc++.h>
using namespace std;
typedef signed long long ll;

#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define FORR2(x,y,arr) for(auto& [x,y]:arr)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
template<class T> bool chmax(T &a, const T &b) { if(a<b){a=b;return 1;}return 0;}
template<class T> bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;}
//-------------------------------------------------------

int N;
ll A[202020],B[202020];

void solve() {
	int i,j,k,l,r,x,y; string s;
	
	cin>>N;
	FOR(i,N) cin>>A[i];
	FOR(i,N) cin>>B[i];
	
	vector<ll> X,Y;
	X={A[0]};
	Y={B[0]};
	for(i=1;i<N;i++) {
		ll a=A[i];
		ll b=B[i];
		while(X.size()&&X.back()*b>Y.back()*a) {
			a+=X.back();
			b+=Y.back();
			X.pop_back();
			Y.pop_back();
		}
		X.push_back(a);
		Y.push_back(b);
	}
	double cur=1;
	double sum=0;
	FOR(i,X.size()) {
		if(X[i]>Y[i]) {
			double best=sqrt((double)X[i]/Y[i]);
			cur=max(best,cur);
		}
		sum+=X[i]/cur+Y[i]*cur;
	}
	_P("%.12lf\n",sum);
	
}


int main(int argc,char** argv){
	string s;int i;
	if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
	FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
	cout.tie(0); solve(); return 0;
}