1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #include<cmath>
 5 const int maxn=262145;
 6 const int inf=0x3f3f3f3f;
 7 const double pi = acos(-1.0);
 8
 9 int tim[maxn];
10
11 namespace FFT {
12     struct Complex {
13         double r,i;
14         friend Complex operator + (const Complex &a,const Complex &b) { return (Complex){a.r+b.r,a.i+b.i}; }
15         friend Complex operator - (const Complex &a,const Complex &b) { return (Complex){a.r-b.r,a.i-b.i}; }
16         friend Complex operator * (const Complex &a,const Complex &b) { return (Complex){a.r*b.r-a.i*b.i,a.r*b.i+a.i*b.r}; }
17     }cp[maxn];
18     inline void FFT(Complex* dst,int n,int tpe) {
19         for(int i=0,j=0;i<n;i++) {
20             if( i < j ) std::swap(dst[i],dst[j]);
21             for(int t=n>>1;(j^=t)<t;t>>=1) ;
22         }
23         for(int len=2;len<=n;len<<=1) {
24             const int h = len >> 1;
25             const Complex per = (Complex){cos(pi*tpe/h),sin(pi*tpe/h)};
26             for(int st=0;st<n;st+=len) {
27                 Complex w = (Complex){1.0,0.0};
28                 for(int pos=0;pos<h;pos++) {
29                     const Complex u = dst[st+pos] , v = dst[st+pos+h] * w;
30                     dst[st+pos] = u + v , dst[st+pos+h] = u - v , w = w * per;
31                 }
32             }
33         }
34         if( !~tpe ) for(int i=0;i<n;i++) dst[i].r /= n;
35     }
36     inline void mul(int* dst,int n) {
37         int len = 1;
38         while( len <= ( n << 1 ) ) len <<= 1;
39         for(int i=0;i<len;i++) cp[i] = (Complex){(double)dst[i],0.0};
40         FFT(cp,len,1);
41         for(int i=0;i<len;i++) cp[i] = cp[i] * cp[i];
42         FFT(cp,len,-1);
43         for(int i=0;i<len;i++) dst[i] = (int)(cp[i].r+0.5);
44     }
45 }
46
47 namespace Tree {
48     int s[maxn],t[maxn<<1],nxt[maxn<<1];
49     int siz[maxn],mxs[maxn],ban[maxn];
50     int su[maxn],tp[maxn];
51
52     inline void addedge(int from,int to) {
53         static int cnt = 0;
54         t[++cnt] = to , nxt[cnt] = s[from] , s[from] = cnt;
55     }
56     inline void findroot(int pos,int fa,const int &fs,int &rt) {
57         siz[pos] = 1 , mxs[pos] = 0;
58         for(int at=s[pos];at;at=nxt[at]) if( t[at] != fa && !ban[t[at]] ) findroot(t[at],pos,fs,rt) , siz[pos] += siz[t[at]] , mxs[pos] = std::max( mxs[pos] , siz[t[at]] );
59         if( ( mxs[pos] = std::max( mxs[pos] , fs - siz[pos]) ) <= mxs[rt] ) rt = pos;
60     }
61     inline void dfs(int pos,int fa,int dep,int &mxd) {
62         mxd = std::max( mxd , dep ) , ++tp[dep];
63         for(int at=s[pos];at;at=nxt[at]) if( t[at] != fa && !ban[t[at]] ) dfs(t[at],pos,dep+1,mxd);
64     }
65     inline void solve(int pos,int fs) {
66         int root = 0 , mxd = 0 , ths ;
67         *mxs = inf, findroot(pos,-1,fs,root) , ban[root] = 1;
68         for(int at=s[root];at;at=nxt[at]) if( !ban[t[at]]) {
69             ths = 0 , dfs(t[at],root,1,ths) , mxd = std::max( mxd , ths );
70             for(int i=1;i<=ths;i++) su[i] += tp[i];
71             FFT::mul(tp,ths);
72             for(int i=1;i<=ths<<1;i++) tim[i] -= tp[i];
73             memset(tp,0,sizeof(int)*(ths<<1|1));
74         }
75         ++*su , FFT::mul(su,mxd);
76         for(int i=1;i<=mxd<<1;i++) tim[i] += su[i];
77         memset(su,0,sizeof(int)*(mxd<<1|1));
78         for(int at=s[root];at;at=nxt[at]) if( !ban[t[at]] ) solve(t[at],siz[t[at]]<siz[root]?siz[t[at]]:fs-siz[root]);
79     }
80 }
81
82 int main() {
83     static int n;
84     static long double ans;
85     scanf("%d",&n);
86     for(int i=1,a,b;i<n;i++) scanf("%d%d",&a,&b) , ++a , ++b , Tree::addedge(a,b) , Tree::addedge(b,a);
87     Tree::solve(1,n) , ans = n;
88     for(int i=1;i<=n<<1;i++) ans += (long double) tim[i] / ( i + 1 );
89     printf("%0.4Lf\n",ans);
90     return 0;
91 }