#include <bits/stdc++.h>
#include <tr1/unordered_map>
#define ri register int
using namespace std;
typedef double db;
typedef long double ld;
typedef long long ll;
typedef vector <int> poly;
typedef pair <int, int> pii;
typedef pair <ll, int> pli;
typedef pair <int, ll> pil;
typedef pair <ll, ll> pll;
typedef unsigned long long ulll;
typedef unsigned int uii;
typedef string strr;
#define fi first
#define se second
#define pb push_back
#define ppp pop_back
#define rez resize
#define hhh cout << '\n';
#define dhhh cerr << '\n';
#define jhhh cout << endl;
const ll Inf = 2e18;
const int rlen = 1 << 20, inf = 0x3f3f3f3f;
char buf[rlen], *ib = buf, *ob = buf;
#define gc() (((ib == ob) && (ob = (ib =  buf) + fread(buf, 1, rlen, stdin)), ib == ob) ? -1 : *ib++)
inline int read() {
  static int ans, f;
  static char ch;
  ans = 0, ch = gc(), f = 1;
  while (!isdigit(ch)) f ^= ch == '-', ch = gc();
  while (isdigit(ch)) ans = (ans << 3) + (ans << 1) + (ch ^ 48), ch = gc();
  return f ? ans: -ans;
}
inline ll readl() {
  static ll ans;
  static char ch;
  for (ans = 0, ch = gc(); !isdigit(ch); ch = gc());
  while (isdigit(ch)) ans = ((ans << 2) + ans << 1) + (ch ^ 48), ch = gc();
  return ans;
}
inline int Read(char *s) {
  static int top;
  static char ch;
  top = 0, ch = gc();
  while (!isalpha(ch) && !isdigit(ch)) ch = gc();
  while (isalpha(ch) || isdigit(ch)) s[++top] = ch, ch = gc();
  return top;
}
namespace modular {
  const int mod = 998244353;//= 1e9 + 7;
  //int mod;
  int ret;
  inline int add(int a, int b) { return a + b < mod ? a + b : a + b - mod; }
  inline int dec(int a, int b) { return a < b ? a - b + mod : a - b; }
  inline int mul(int a, int b) { return (ll) a * b % mod; }
  inline void Add(int &a, int b) { a = a + b < mod ? a + b : a + b - mod; }
  inline void Dec(int &a, int b) { a = a < b? a - b + mod : a - b; }
  inline void Mul(int &a, int b) { a = (ll) a * b % mod; }
  inline int ksm(int a, int p) {
    for (ret = 1; p; p >>= 1, Mul(a, a)) (p & 1) && (Mul(ret, a), 1);
    return ret;
  }
  inline int Inv(int a) { return ksm(a, mod - 2); }
  inline int sqr(int a) { return (ll) a * a % mod; }
  inline int cub(int a) { return (ll) a * a % mod * a % mod; }
} using namespace modular;
template <typename T> inline void ckmax(T &a, T b) { a < b ? a = b : 0; }
template <typename T> inline void ckmin(T &a, T b) { a > b ? a = b : 0; }
template <typename T> inline T Abs(T a) { return a < 0 ? -a : a; }
template <typename T> inline T gcd(T a, T b) {
  T t;
  while (b) t = a, a = b, b = t - t / a * a;
  return a;
}
template <typename T> inline void exgcd(T a, T b, T &x, T &y) {
  if (!b) {
    x = 1, y = 0;
    return;
  }
  exgcd(b, a - a / b * b, y, x);
  y -= a / b * x;
}
const int N = 2e5 + 5;
struct pt {
  ll x, y;
  pt(ll x = 0, ll y = 0) : x(x), y(y) {}
  inline pt operator + (pt a) { return pt(x + a.x, y + a.y); }
  inline pt operator - (pt a) { return pt(x - a.x, y - a.y); }
  inline ll operator ^ (pt a) { return x * a.y - y * a.x; }
} vl[N];
int n, top, b[N], _b[N], q[N];
ll a[N], c[N], _a[N];
int main() {
  #ifdef ldxcaicai
  freopen("lx.in", "r", stdin);
  #endif
  n = read();
  for (ri i = 1; i <= n; ++i) _a[i] = readl();
  for (ri i = 1; i <= n; ++i) _b[i] = read();
  int ps = 1;
  for (ri i = 2; i <= n; ++i) if (_a[i] > _a[ps]) ps = i;
  int sig = -1;
  for (ri i = ps; i <= n; ++i) a[++sig] = _a[i];
  for (ri i = 1; i < ps; ++i) a[++sig] = _a[i];
  a[++sig] = a[0];
  sig = -1;
  for (ri i = ps; i <= n; ++i) b[++sig] = _b[i];
  for (ri i = 1; i < ps; ++i) b[++sig] = _b[i];
  b[++sig] = b[0];
  for (ri i = 2; i <= n; ++i) c[i] = 2 * (c[i - 1] + b[i - 1]) - c[i - 2];
  for (ri i = 0; i <= n; ++i) {
    vl[i] = pt(i, a[i] - c[i]);
    while (top > 1 && ((vl[q[top]] - vl[q[top - 1]]) ^ (vl[i] - vl[q[top - 1]])) >= 0) --top;
    q[++top] = i;
  }
  ll res = 0;
  for (ri i = 2; i <= top; ++i) res += (q[i] - q[i - 1] + 1) * vl[q[i - 1]].y + (q[i] - q[i - 1] - 1) * vl[q[i]].y;
  for (ri i = 0; i < n; ++i) res += 2 * c[i];
  printf("%.15lf", (double) res / (n * 2));
  return 0;
}

Measured memory_bytes: 14848