#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
constexpr ll MAX = 2e3;

int main(){
  int n;
  cin >> n;
  vector<ll> a(n), r(n), cnt(MAX);
  rep(i,n) {
    cin >> a[i];
    cnt[a[i]]++;
  }
  rep(i,n) cin >> r[i];
  sort(a.begin(),a.end());
  vector<vector<double>> dp(n,vector<double>(n,0.0));
  rep(i,n) dp[i][i] = 1.0; 
  double ans = 0;
  rep(i,n) {
    rep(j,n) ans += dp[j][0]*a[j]*r[i]/2.0;
    vector<vector<double>> dpn(n,vector<double>(n,0.0));
    rep(j,n) rep(k,n) {
      dpn[j][k] += dp[j][k]/2.0;
      if(k+1 < n) dpn[j][k] += dp[j][k+1]/2.0;
    }
    swap(dp,dpn);
  }
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}