Momiji has got a rooted tree, consisting of *n* nodes. The tree nodes are numbered by integers from 1 to *n*. The root has number 1. Momiji decided to play a game on this tree.

The game consists of several steps. On each step, Momiji chooses one of the remaining tree nodes (let's denote it by *v*) and removes all the subtree nodes with the root in node *v* from the tree. Node *v* gets deleted as well. The game finishes when the tree has no nodes left. In other words, the game finishes after the step that chooses the node number 1.

Each time Momiji chooses a new node uniformly among all the remaining nodes. Your task is to find the expectation of the number of steps in the described game.
The first line contains integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>) — the number of nodes in the tree. The next *n* - 1 lines contain the tree edges. The *i*-th line contains integers *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub> ≤ *n*; *a*<sub class="lower-index">*i*</sub> ≠ *b*<sub class="lower-index">*i*</sub>) — the numbers of the nodes that are connected by the *i*-th edge.

It is guaranteed that the given graph is a tree.
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <sstream>
#include <iomanip>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <algorithm>
using namespace std;

#define nln        puts("")                         ///printnewline
#define getint(a)  scanf("%d",&a);
#define max3(a,b,c) max(a,max(b,c))                  ///3 ta theke max
#define min3(a,b,c) min(a,min(b,c))                  ///3 ta theke min

#define FOR1(i,n)  for(int i=1;i<=n;i++)
#define FOR0(i,n)  for(int i=0;i<n;i++)                 ///looping
#define FORR(i,n)  for(int i=n-1;i>=0;i--)
#define ALL(p)     p.begin(),p.end()

#define SET(p)     memset(p,-1,sizeof(p))
#define CLR(p)     memset(p,0,sizeof(p))            ///memset
#define MEM(p,v)   memset(p,v,sizeof(p))

#define READ(f)    freopen(f, "r", stdin)           /// file
#define WRITE(f)   freopen(f, "w", stdout)

#define SZ(c)      (int)c.size()
#define PB(x)      push_back(x)                     ///STL defines
#define MP(x,y)    make_pair(x,y)
#define ff         first
#define ss         second

#define LI         long int
#define LLI        long long int
#define f64        long double
#define PI         acos(-1.0)                        ///PI er value

int Set(int N,int pos)
{
    return N=N | (1<<pos);
}
int reset(int N,int pos)
{
    return N= N & ~(1<<pos);
}
bool check(int N,int pos)
{
    return (bool)(N & (1<<pos));
}
void CI(int &_x)
{
    scanf("%d",&_x);
}

void CO(int &_x)
{
    cout<<_x;
}

template<typename T> void getarray(T a[],int n)
{
    for(int i=0; i<n; i++) cin>>a[i];
}
template<typename T> void printarray(T a[],int n)
{
    for(int i=0; i<n-1; i++) cout<<a[i]<<" ";
    cout<<a[n-1]<<endl;
}

const double EPS=1e-9;                              ///constatnts
const int INF=0x7f7f7f7f;

int dr8[8]= {1,-1,0,0,1,-1,-1,1};            ///8 direction move
int dc8[8]= {0,0,-1,1,1,1,-1,-1};
int dr4[4]= {0,0,1,-1};                      ///4 direction move
int dc4[4]= {-1,1,0,0};                      ///or adjacent dir.
int kn8r[8]= {1,2,2,1,-1,-2,-2,-1};          ///knight moves
int kn8c[8]= {2,1,-1,-2,-2,-1,1,2};
#define mx 100005
vector<int>G[mx];
double ans=0;
void dfs(int u,int par,int kount)
{

    ans+=1.0/(1.0*kount);

    for(int i=0; i<G[u].size(); i++)
    {

        int v=G[u][i];
        if(v==par)continue;
        dfs(v,u,kount+1);
    }

//   cout<<u<<" "<<par<<" "


}
int main()
{

    int n;
    cin>>n;
    FOR1(i,n-1)
    {
        int a,b;
        cin>>a>>b;
        G[a].PB(b);
        G[b].PB(a);
    }
    dfs(1,1,1);
    cout<<ans<<"\n";
}
