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 #include <bits/stdc++.h>
using namespace std;
const int maxn = 30005; const int maxp = 270005; const double PI = acos(1.0);
struct comp { double r, i; comp(double r_ = 0.0, double i_ = 0.0) : r(r_), i(i_) {} inline comp operator+(comp rhs) { return comp(r + rhs.r, i + rhs.i); } inline comp operator(comp rhs) { return comp(r  rhs.r, i  rhs.i); } inline comp operator*(comp rhs) { return comp(r * rhs.r  i * rhs.i, r * rhs.i + i * rhs.r); } inline comp conj() { return comp(r, i); } }omega[maxp], _omega[maxp], A[maxp]; struct edge { int to, nxt; }e[maxn << 1]; int n, ptr, lnk[maxn], vis[maxn], mx[maxn]; int siz[maxn], sum, glbmn, rt; int d[maxn], tot; int rev[maxp]; int bkt[maxn << 2];
inline int rd() { register int x = 0, c = getchar(); while (!isdigit(c)) c = getchar(); while(isdigit(c)) x = x * 10 + (c ^ 48), c = getchar(); return x; } inline void add(int bgn, int end) { e[++ptr] = (edge){end, lnk[bgn]}; lnk[bgn] = ptr; } inline void FFT(comp *a, int N, int L, int typ) { for (int i = 0; i < N; ++i) rev[i] = (rev[i >> 1] >> 1)  ((i & 1) << (L  1)); double round = 2.0 * PI / N; for (int i = 0; i < N; ++i) { if (typ == 1) { omega[i] = comp(cos(i * round), sin(i * round)); } else { _omega[i] = comp(cos(i * round), 1.0 * sin(i * round)); } } comp *w = NULL; if (typ == 1) w = omega; else w = _omega; for (int i = 0; i < N; ++i) if (i > rev[i]) swap(a[i], a[rev[i]]); for (int i = 2; i <= N; i <<= 1) { int m = (i >> 1); for (int j = 0; j < N; j += i) { for (int k = 0; k < m; ++k) { comp t = a[j + m + k] * w[N / i * k]; a[j + m + k] = a[j + k]  t; a[j + k] = a[j + k] + t; } } } if (typ == 1) { for (int i = 0; i < N; ++i) a[i].r /= N; } } void getroot(int x, int fa) { siz[x] = 1; mx[x] = 0; for (int p = lnk[x]; p; p = e[p].nxt) { int y = e[p].to; if (y == fa  vis[y]) continue; getroot(y, x); siz[x] += siz[y]; mx[x] = max(mx[x], siz[y]); } mx[x] = max(mx[x], sum  siz[x]); if (mx[x] < glbmn) glbmn = mx[x], rt = x; } void getdep(int x, int fa, int dep) { d[++tot] = dep; for (int p = lnk[x]; p; p = e[p].nxt) { int y = e[p].to; if (y == fa  vis[y]) continue; getdep(y, x, dep + 1); } } void calc(int x, int dep, int tg) { tot = 0; getdep(x, 0, dep); int mxv = 0; for (int i = 1; i <= tot; ++i) mxv = max(mxv, d[i]); int N = 1, L = 0; while (N <= 2 * mxv) N <<= 1, L++; for (int i = 0; i < N; ++i) A[i].r = A[i].i = 0; for (int i = 1; i <= tot; ++i) A[d[i]].r++; FFT(A, N, L, 1); for (int i = 0; i < N; ++i) A[i] = A[i] * A[i]; FFT(A, N, L, 1); for (int i = 0; i <= 2 * mxv; ++i) { if (tg) bkt[i] = (int)(A[i].r + 0.5); else bkt[i] += (int)(A[i].r + 0.5); } } void solve(int x) { vis[x] = 1; calc(x, 0, 0); for (int p = lnk[x]; p; p = e[p].nxt) { int y = e[p].to; if (vis[y]) continue; calc(y, 1, 1); glbmn = 0x3f3f3f3f; rt = 0; sum = siz[y]; getroot(y, 0); solve(rt); } }
int main() { n = rd(); int u, v; for (int i = 1; i < n; ++i) { u = rd(); v = rd(); ++u; ++v; add(u, v); add(v, u); } glbmn = 0x3f3f3f3f; rt = 0; sum = n; getroot(1, 0); solve(rt); long double ans = 0.0; for (int i = 0; i < n; ++i) { ans += (long double)bkt[i] / (i + 1); } printf("%.4Lf\n", ans); return 0; }
