Problem: There are n cities and n - 1 roads in the Seven Kingdoms, each road connects two cities and we can reach any city from any other by the roads.

Theon and Yara Greyjoy are on a horse in the first city, they are starting traveling through the roads. But the weather is foggy, so they can’t see where the horse brings them. When the horse reaches a city (including the first one), it goes to one of the cities connected to the current city. But it is a strange horse, it only goes to cities in which they weren't before. In each such city, the horse goes with equal probabilities and it stops when there are no such cities. 

Let the length of each road be 1. The journey starts in the city 1. What is the expected length (expected value of length) of their journey? You can read about expected (average) value by the link <https://en.wikipedia.org/wiki/Expected_value>.

Input

The first line contains a single integer n (1 ≤ n ≤ 100000) — number of cities.

Then n - 1 lines follow. The i-th line of these lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the cities connected by the i-th road.

It is guaranteed that one can reach any city from any other by the roads.

Output

Print a number — the expected length of their journey. The journey starts in the city 1.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

4
1 2
1 3
2 4


Output

1.500000000000000


Input

5
1 2
1 3
3 4
2 5


Output

2.000000000000000

Note

In the first sample, their journey may end in cities 3 or 4 with equal probability. The distance to city 3 is 1 and to city 4 is 2, so the expected length is 1.5.

In the second sample, their journey may end in city 4 or 5. The distance to the both cities is 2, so the expected length is 2.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
 
 
public class gfg {
    static int n;
    static int m;
    static ArrayList<Integer>[] graph;
    static boolean[] vis;
    static boolean minus=false;
    static int paths=0;
    static double sum=0.0;
    static int[] level;
    static HashSet<Integer> set1 = new HashSet<>();
    static HashSet<Integer> set2 = new HashSet<>();
    static HashMap<Integer,Integer> map = new HashMap<>();
 
    static void solve(){
        
    }
    static void dfs(int x,double value){
        vis[x]=true;
        if(graph[x].size()==1){
            sum+=value*level[x];
        }
        for(int i=0;i<graph[x].size();i++){
            int a = graph[x].get(i);
            if(!vis[a]){
                level[a]=level[x]+1;
                if(x==1)
                    dfs(a,value*(double)1/graph[x].size());
                else
                    dfs(a,value*(double)1/(graph[x].size()-1));
            }
        }
    }
    public static void main(String[] args) throws IOException{
        Reader r = new Reader();
        Reader.init(System.in);
        n = r.nextInt();
        m = n-1;
        graph = new ArrayList[n+1];
        vis = new boolean[n+1];
        level = new int[n+1];
        for(int i=1;i<=n;i++){
            graph[i] = new ArrayList<>();
        }
        for(int i=1;i<=m;i++){
            int a = r.nextInt();
            int b  = r.nextInt();
            graph[a].add(b);
            graph[b].add(a);
        }
        dfs(1,1.0);
        if(n==1)
            sum=0.0;
        System.out.println(sum);
        
    }
    // ggratest common divisor
    static int gcd(int a , int b){
        if(b==0)
            return a;
        else
            return gcd(b,a%b);
    }
 
    // least common multiple
    static int lcm(int a, int b){
        return (a*b)/gcd(a,b);
    }
    
    // a^b
    static long fastpow(long a, long n){
        //System.out.println("ssdf");
        if(n>0){
            long half = fastpow(a,n/2);
            if(n%2==0){
                return half*half;
            } 
            else
                return a*half*half;
        }
        return 1;
    }
 
    
}
 
 
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
 
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
 
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
 
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
class newcomparator implements Comparator<Integer>{
    //@Override
    public int compare(Integer a, Integer  b){
        return a<=b?1:-1;
    }
 }
class node {
    int a;
    long b;// cost to rreach\
    node(int s,long va){
        a=s;
        b=va;
    }
}
class mergesort{
    static void sort(int l, int h, int[] arr){
        if(l<h){
            int mid = (l+h)/2;
            
            sort(l,mid,arr);
            sort(mid+1,h,arr);
            merge(l,mid,h,arr);
        }
    }
    static void merge(int l, int m , int h , int [] arr){
 
        int[] left = new int[m-l+1];
        int[] right = new int[h-m];
        for(int i= 0 ;i< m-l+1;i++){
            left[i] = arr[l+i];
        }
        for(int i=0;i<h-m;i++){
            right[i] = arr[m+1+i];
        }
        //now left and right arrays are assumed to be sorted and we have tp merge them together 
        // int the original aaray.
        int i=l;
        int lindex = 0;
        int rindex =  0;
        
        while(lindex<m-l+1 && rindex<h-m){
            if(left[lindex]<=right[rindex]){
                arr[i]=left[lindex];
                lindex++;
                i++;
            }
            else{
                arr[i]=right[rindex];
                rindex++;
                i++;
            }
        }
        while(lindex<m-l+1){
            arr[i]=left[lindex];
            lindex++;
            i++;
        }
        while(rindex<h-m){
            arr[i]=right[rindex];
            rindex++;
            i++;
        }
    }
    
}