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.io.*;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
import java.util.Map.Entry;
import java.util.regex.Pattern;

import javax.management.relation.RelationServiceNotRegisteredException;


public class hehehe {

	static int count=0;
	static int flag=0;
	static double eps=(double)1e-6;
	static long mod=(long)1e9+7;
	static int maxcount=0;
	static int index=0;
	static int fac[]=new int[10];
	static int end_time[]=new int[100001];
	static int bit[]=new int[100001];
	static int vis_time[]=new int[100001];
	static int flat_tree[]=new int[200001];
	static ArrayList<ArrayList<Integer>> tree=new ArrayList<>();
	static ArrayList<ArrayList<Integer>> table=new ArrayList<>();
	static int traverser[]=new int[100001];
	static int par[]=new int[100001];
	static boolean vis[]=new boolean[100001];
	static int tim = 0;

	//li, ri and index are stored in queries vector
	//in that order, as the sort function will use
	//the value li for comparison
	static ArrayList< pair1 > queries=new ArrayList<>();

	//ans[i] stores answer to ith query
	static int ans[]=new int[100001];
	static HashSet<String> hm;

	public static void main(String args[]){
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		Scanner sc=new Scanner(System.in);
		//----------My Code----------
		Queue<Pair> a=new LinkedList<Pair>();
		int n=in.nextInt();
		int visited[]=new int[n+1];
		ArrayList<ArrayList<Integer>> arr=new ArrayList<>();
		for(int i=0;i<=n;i++)
			arr.add(new ArrayList<Integer>());
		for(int i=0;i<n-1;i++){
			int x=in.nextInt();
			int y=in.nextInt();
			arr.get(x).add(y);
			arr.get(y).add(x);
		}
		int par[]=new int[n+1];
		a.add(new Pair(1,1,0));
		par[1]=0;
		double ans=0;
		while(!a.isEmpty()){
			Pair p=a.poll();
			int pop=p.x;
			if(visited[pop]==0){
				int val=0;
				
				//System.out.println(arr.get(pop).size());
			for(int i=0;i<arr.get(pop).size();i++){
				int ele=arr.get(pop).get(i);
				
				if(visited[ele]==0)	{
				par[ele]=pop;
				if(pop!=1)
				a.add(new Pair(ele,p.y*(((double)1/(arr.get(pop).size()-1))),p.z+1));
				else
					a.add(new Pair(ele,p.y*(((double)1/(arr.get(pop).size()))),p.z+1));
				}
				else
					val++;
			}
			if(val==arr.get(pop).size()){
				ans+=p.y*p.z;
				
			//System.out.println(p.y+" "+p.z+""+pop);
			}
			}
			visited[pop]=1;
		}
		System.out.println(ans);
		//-- -------------The End----------------- 	-
		out.close();
	}
	
	static int rec(String ans,int length){
		if(length<=2){
			return 0;
		}
		else{
			
			int flag=0;
		char start=ans.charAt(0);
		for(int i=1;i<ans.length()-1;i++){
       	 if(start=='0'&&ans.charAt(i+1)=='0'){
                if(ans.charAt(i)=='0'){
                    flag=1;
                  //  System.out.println(ans.substring(0, i)+ans.substring(i+1));
                   count=count^rec(ans.substring(0, i)+ans.substring(i+1),ans.length()-1);
                }
                else if (ans.charAt(i)=='1'){
                     flag=1;
                   //  System.out.println(ans.substring(0, i)+ans.substring(i+1));
                	 count=count^rec(ans.substring(0, i)+ans.substring(i+1),ans.length()-1);
                 
                }
               
            }
       	 start=ans.charAt(i);
        }
		if(flag==0)
			return count^1;
		return count;
		}	
	}
	
	static int recursiveBinarySearch(int[] sortedArray, int start, int end, int key) {

		while (start < end) {
			int mid = start + (end - start) / 2; 
			if (key < sortedArray[mid]) {
				end=mid-1;

			} else if (key >=sortedArray[mid]) {
				start=mid+1;
			}
		}
		return (start); 
	}

	static long modulo(long a,long b,long c) {
		long x=1;
		long y=a;
		while(b > 0){
			if(b%2 == 1){
				x=(x*y)%c;
			}

			y = (y*y)%c; // squaring the base
			b /= 2;
		}
		return  x%c;
	}


	static long gcd(long x, long y)

	{
		if(x==0||y==0)
			return 0;
		long r=0, a, b;
		a = (x > y) ? x : y; // a is greater number
		b = (x < y) ? x : y; // b is smaller number
		r = b;
		while(a % b != 0)
		{
			r = a % b;
			a = b;
			b = r;
		}
		return r;
	}
	static class Pair  {
		int x;
		double y;
		int z;
		//int i;
		Pair(int  xx,double yy,int zz){

			x=xx;
			y=yy;
			//i=ii;
			z=zz;
		}
		
		

	}
	static class pair1 implements Comparable<pair1>{
		Pair p;
		int x;
		pair1(Pair p,int x){
			this.p=p;
			this.x=x;
		}
		public int compareTo(pair1 arg0) {



			return Integer.compare(p.x, arg0.p.x);


		}

	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine(){
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}