/**
 *    author:  tourist
 *    created: 23.05.2020 16:09:07       
**/
#include <bits/stdc++.h>

using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char* s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

typedef long double ld;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<long long> 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];
  }
  int shift = (int) (max_element(a.begin(), a.end()) - a.begin());
  rotate(a.begin(), a.begin() + shift, a.end());
  rotate(b.begin(), b.begin() + shift, b.end());
  a.push_back(a[0]);
  b.push_back(b[0]);
  vector<long long> pref_b(n + 2);
  for (int i = 0; i <= n; i++) {
    pref_b[i + 1] = pref_b[i] + b[i];
  }
  vector<long long> pref_bi(n + 2);
  for (int i = 0; i <= n; i++) {
    pref_bi[i + 1] = pref_bi[i] + b[i] * i;
  }
  auto Calc = [&](int j, int i) {
    // j -> i
    int dist = abs(j - i);
    ld sum = 0;
    sum += a[j] * (dist - 1);
    sum += a[i];
    if (j > i) {
      sum += (pref_b[j] - pref_b[i + 1]) * i * 2;
      sum -= (pref_bi[j] - pref_bi[i + 1]) * 2;
    } else {
      sum -= (pref_b[i] - pref_b[j + 1]) * i * 2;
      sum += (pref_bi[i] - pref_bi[j + 1]) * 2;
    }
    return (ld) sum / (ld) dist;
  };
  auto Eliminate = [&](int i, int j, int k) {
    ld x = Calc(j, i);
    ld y = Calc(j, k);
    return (x + y - 2 * b[j] > 2 * a[j]);
  };
  vector<int> st(1, 0);
  for (int i = 1; i <= n; i++) {
    while (st.size() > 1) {
      if (Eliminate(st[st.size() - 2], st.back(), i)) {
        st.pop_back();
      } else {
        break;
      }
    }
    st.push_back(i);
  }
  debug(st);
  ld ans = 0;
  for (int it = 0; it < (int) st.size() - 1; it++) {
    int i = st[it];
    int j = st[it + 1];
    ld pr = a[i];
    ld x = Calc(i, j);
    for (int k = i + 1; k <= j; k++) {
      ans += x;
      debug(k, x);
      ld new_x = 2 * x - pr + 2 * b[k];
      pr = x;
      x = new_x;
    }
    debug(a[j]);
  }
  ans /= n;
  cout << fixed << setprecision(17) << ans << '\n';
  return 0;
}


Measured memory_bytes: 10396