#include <bits/stdc++.h>
using namespace std;
const double INF = 1000000000;
int main(){
  cout << fixed << setprecision(20);
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++){
    cin >> A[i];
  }
  vector<int> B(N);
  for (int i = 0; i < N; i++){
    cin >> B[i];
  }
  vector<long long> SA(N + 1), SB(N + 1);
  SA[N] = 0;
  SB[N] = 0;
  for (int i = N - 1; i >= 0; i--){
    SA[i] = SA[i + 1] + A[i];
    SB[i] = SB[i + 1] + B[i];
  }
  vector<double> X;
  for (int i = 0; i < N; i++){
    double x = sqrt((double) SA[i] / SB[i]);
    if (x > 1){
      X.push_back(x);
    }
  }
  X.push_back(1);
  sort(X.begin(), X.end());
  int M = X.size();
  vector<double> dp(M, 0);
  for (int i = N - 1; i >= 0; i--){
    for (int j = 0; j < M; j++){
      dp[j] += A[i] / X[j] + B[i] * X[j];
    }
    for (int j = M - 2; j >= 0; j--){
      dp[j] = min(dp[j], dp[j + 1]);
    }
  }
  cout << dp[0] << endl;
}