#include <bits/stdc++.h>
using std::max;
using std::min;
const int inf = 0x3f3f3f3f, Inf = 0x7fffffff;
const long long INF = 0x3f3f3f3f3f3f3f3f;
std::mt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());
template <typename _Tp>
_Tp gcd(const _Tp &a, const _Tp &b) {
  return (!b) ? a : gcd(b, a % b);
}
template <typename _Tp>
inline _Tp abs(const _Tp &a) {
  return a >= 0 ? a : -a;
}
template <typename _Tp>
inline void chmax(_Tp &a, const _Tp &b) {
  (a < b) && (a = b);
}
template <typename _Tp>
inline void chmin(_Tp &a, const _Tp &b) {
  (b < a) && (a = b);
}
template <typename _Tp>
inline void read(_Tp &x) {
  char ch(getchar());
  bool f(false);
  while (!isdigit(ch)) f |= ch == 45, ch = getchar();
  x = ch & 15, ch = getchar();
  while (isdigit(ch)) x = (((x << 2) + x) << 1) + (ch & 15), ch = getchar();
  f && (x = -x);
}
template <typename _Tp, typename... Args>
inline void read(_Tp &t, Args &...args) {
  read(t);
  read(args...);
}
inline int read_str(char *s) {
  char ch(getchar());
  while (ch == ' ' || ch == '\r' || ch == '\n') ch = getchar();
  char *tar = s;
  *tar++ = ch, ch = getchar();
  while (ch != ' ' && ch != '\r' && ch != '\n' && ch != EOF)
    *tar++ = ch, ch = getchar();
  return *tar = 0, tar - s;
}
const int N = 3005;
struct edge {
  int v, nxt;
} c[N << 1];
int front[N], edge_cnt;
inline void addedge(int u, int v) {
  c[++edge_cnt] = (edge){v, front[u]};
  front[u] = edge_cnt;
}
int st[N], top;
bool vis[N];
int loop[N], pos, id[N];
void dfs1(int x, int fa) {
  if (pos) return;
  if (vis[x]) {
    while (st[top] != x) {
      int tmp = st[top--];
      loop[++pos] = tmp;
    }
    loop[++pos] = x;
    return;
  }
  st[++top] = x, vis[x] = true;
  for (int i = front[x]; i; i = c[i].nxt) {
    int v = c[i].v;
    if (v == fa) continue;
    dfs1(v, x);
  }
  if (pos) return;
  --top, vis[x] = false;
}
int dis[N];
void dfs2(int x, int fa) {
  dis[x] = dis[fa] + 1;
  if (fa) id[x] = id[fa];
  for (int i = front[x]; i; i = c[i].nxt) {
    int v = c[i].v;
    if (v == fa || id[v]) continue;
    dfs2(v, x);
  }
}
double ans;
void dfs3(int x, int fa, int len) {
  ans += 1.0 / (++len);
  for (int i = front[x]; i; i = c[i].nxt) {
    int v = c[i].v;
    if (v == fa || id[v] != id[x]) continue;
    dfs3(v, x, len);
  }
}
inline double f(int a, int b, int c, int d) {
  return (1.0 * b / (a + c + d) + 1.0 * c / (a + b + d) + 1) / (a + b + c + d);
}
int main() {
  int n;
  read(n);
  int x, y;
  for (int i = 1; i <= n; ++i)
    read(x, y), ++x, ++y, addedge(x, y), addedge(y, x);
  dfs1(1, 0);
  for (int i = 1; i <= pos; ++i) id[loop[i]] = i;
  for (int i = 1; i <= pos; ++i) dfs2(loop[i], 0);
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j)
      if (id[i] != id[j])
        ans += f(dis[i], abs(id[i] - id[j]) - 1, pos - abs(id[i] - id[j]) - 1,
                 dis[j]);
  for (int i = 1; i <= n; ++i) dfs3(i, 0, 0);
  printf("%.8lf\n", ans);
  return 0;
}
