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.*;
import java.math.*;

public class C{
	
	static int n;
	static ArrayList<Integer>e[];
	static double p[],dist[];
	static boolean d[],isL[];
	static double res;
	static void bfs(){
		p=new double[n+2]; Arrays.fill(p, 0.0);
		dist=new double[n+2]; Arrays.fill(dist, 0.0);
		d=new boolean[n+2]; Arrays.fill(d, false);
		isL=new boolean[n+2]; Arrays.fill(isL, true);
		ArrayList<Integer> q=new ArrayList<Integer>();
		p[1]=1.0; dist[1]=0;  d[1]=true;
		q.add(1);
		int u,v,j,i,l;
		for (i=0;i<q.size();i++){
			u=q.get(i);
			l=0;
			for (j=0;j<e[u].size();j++){
				if (d[e[u].get(j)]==false){
					l++;
					isL[u]=false;
				}
			}
			if (l>0){
				for (j=0;j<e[u].size();j++){
					v=e[u].get(j);
					if (d[v]==false){
						p[v]=p[u]/((double)l);
						q.add(v);
						d[v]=true;
						dist[v]=dist[u]+1.0;
						isL[v]=true;
					}
				}
			}
		}
		res=0;
		for (u=1;u<=n;u++)if (isL[u]==true)
			res=res+(p[u]*dist[u]);
	}
	static void MainMethod()throws Exception{
		n=reader.nextInt();
		int i,u,v;
		e=new ArrayList[n+2];
		for (i=0;i<=n;i++){
			e[i]=new ArrayList<Integer>();
			e[i].clear();
		}
		for (i=1;i<n;i++){
			u=reader.nextInt();
			v=reader.nextInt();
			e[u].add(v);e[v].add(u);
		}
		res=0;
		bfs();
		printer.printf("%.8f",res);
	}
	public static void main(String[] args)throws Exception{
		MainMethod();
		printer.close();
	}
	static void halt(){
		printer.close();
		System.exit(0);
	}
	static PrintWriter printer=new PrintWriter(new OutputStreamWriter(System.out));
	static class reader{
		static BufferedReader bReader=new BufferedReader(new InputStreamReader(System.in));
		static StringTokenizer token=new StringTokenizer("");
		static String readNextLine() throws Exception{
			return bReader.readLine();
		}
		static String next() throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return token.nextToken();
		}
		static int nextInt()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Integer.parseInt(token.nextToken());
		}
		static long nextLong()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Long.parseLong(token.nextToken());
		}
		static double nextDouble()throws Exception{
			while (token.hasMoreTokens()==false){
				token=new StringTokenizer(bReader.readLine());
			}
			return Double.parseDouble(token.nextToken());
		}
	}
	static class MyMathCompute{
		static long [][] MatrixMultiplyMatrix(long [][] A, long [][] B, long mod) throws Exception{
			int n=A.length, m=B[0].length; 
			int p=A[0].length;
			int i,j,k;
			if (B.length!=p) throw new Exception("invalid matrix input");
			long [][] res=new long [n][m];
			for (i=0;i<n;i++) for (j=0;j<m;j++){
				if (A[i].length!=p) throw new Exception("invalid matrix input");
				res[i][j]=0;
				for (k=0;k<p;k++)
					res[i][j]=(res[i][j]+((A[i][k]*B[k][j])% mod))% mod;
			}
			return res;
		}
		static double [][] MatrixMultiplyMatrix(double [][] A, double [][] B ) throws Exception{
			int n=A.length, m=B[0].length; 
			int p=A[0].length;
			int i,j,k;
			if (B.length!=p) throw new Exception("invalid matrix input");
			double [][] res=new double [n][m];
			for (i=0;i<n;i++) for (j=0;j<m;j++){
				if (A[i].length!=p) throw new Exception("invalid matrix input");
				res[i][j]=0;
				for (k=0;k<p;k++)
					res[i][j]=res[i][j]+(A[i][k]*B[k][j]);
			}
			return res;
		}
		static long [][] MatrixPow(long [][] A,long n, long mod) throws Exception{
			if (n==1) return A;
			long [][] res=MatrixPow(A, n/2, mod);
			res=MatrixMultiplyMatrix(res, res, mod);
			if ((n % 2) == 1) res=MatrixMultiplyMatrix(A,res, mod);		
			return res;
		}
		static double [][] MatrixPow(double [][] A,long n) throws Exception{
			if (n==1) return A;
			double[][] res=MatrixPow(A, n/2);
			res=MatrixMultiplyMatrix(res, res);
			if ((n % 2) == 1) res=MatrixMultiplyMatrix(A,res);		
			return res;
		}
		static long pow(long a,long n,long mod){
			a= a % mod;
			if (n==0) return 1;
			long k=pow(a,n/2,mod);
			if ((n % 2)==0) return ((k*k)%mod);
			else return (((k*k) % mod)*a) % mod;
		}
		static double pow(double a,long n){
			if (n==0) return 1;
			double k=pow(a,n/2);
			if ((n % 2)==0) return (k*k);
			else return (((k*k) )*a) ;
		}
	}
}