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.io.IOException;
import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;
 
 
 
//import sun.net.www.content.audio.wav;
 
import java.text.DecimalFormat;
 
public class Codeforces {
    
    public static long mod = (long)Math.pow(10, 9)+7 ;
    public static double epsilon=0.00000000008854;//value of epsilon
    public static InputReader sc = new InputReader(System.in);
    public static PrintWriter pw = new PrintWriter(System.out);
    
    public static void diji(PriorityQueue<Pair> q,ArrayList<ArrayList<Pair>> a){
        //int vis[]=new int[a.size()];
        boolean vis[]=new boolean[a.size()];
        //vis[0]=1;
        Arrays.fill(vis, false);
        int n=a.size();
        long val[]=new long[n];
 
        long inf=Long.MAX_VALUE;
        Arrays.fill(val, inf);
        q.add(new Pair(0, 0));
        val[0]=0;
        int p[]=new int[n];
        p[0]=-1;
        while(q.size()>0){
            Pair r=q.remove();
            if(vis[r.i])
            continue;
            vis[r.i]=true;///removed
            int u=r.i;
            for(int i=0;i<a.get(u).size();i++){
 
                int v=a.get(u).get(i).i;
                long w=a.get(u).get(i).j;
                    if(val[v]>r.j+w){
                        p[v]=u;
                        val[v]=r.j+w;
                        q.add(new Pair(v, val[v]));
                    }
            }
        }
        //pw.println(Arrays.toString(p));
        int i=n-1;
        Stack<Integer> st=new Stack<>();
        if(val[i]==inf)
        {
            pw.println(-1);
            return;
        }
        while(i!=-1){
            st.add(i+1);
            i=p[i];
        }
        while(st.size()>0){
            pw.print(st.pop()+" ");
        }
        
 
    }
    public static int countSet(int a){
        int c=0;
        while(a>0){
            a&=(a-1);
            c++;
        }
        return c;
    }
    public static void Zfunction(String s){
        int n=s.length();
        int a[]=new int[n];
        int r1=0,r2=1;
        for(int i=1;i<n;){
            int f=0;
            while(r2<n&&s.charAt(r1)==s.charAt(r2)){
                r1++;
                r2++;
            }
            a[i]=r1;
            i++;
            int l2=1;
            for(;i<r2;i++){
                if(i+a[l2]<r2)
                a[i]=a[l2++];
                else{
                    f=1;
                    r1=r2-i;
                    break;
                }
            }
            if(f==0){
                r2=i;
                r1=0;
            }
 
        }
        pw.println(Arrays.toString(a));
    }
    public static void hieghtBfs(int r,int h[],ArrayList<ArrayList <Integer>> a,int p[],int vis[]){/// top to bottom
		Deque<Integer> q=new LinkedList<>();
		q.add(r);
		int c=0;
		p[r]=-1;
		vis[r]=1;
		while(q.size()>0){
			int l=q.size();
			while(l-->0){
				int v=q.remove();
				h[v]=c;
				for(int i=0;i<a.get(v).size();i++){
                    int u=a.get(v).get(i);
                    
					if(vis[u]==0){
                        //pw.print(u+" ");
						p[u]=v;
						vis[u]=1;
						q.add(u);
					}
				}
            }
            //pw.print("\n");
			c++;
		}
    }
    
    public static double hieght(int r,double h[],ArrayList<ArrayList <Integer>> a,int vis[],int p[]){//bottom Up
        vis[r]=1;
        double l=0;
		for(int i=0;i<a.get(r).size();i++){
			int v=a.get(r).get(i);
			if(vis[v]==0){
				p[v]=r;
                h[r]+=hieght(v, h, a, vis,p);
                l++;
			}
        }

        if(l>0){
            //double l=(double)a.get(r).size();
            h[r]/=l;
            h[r]++;
        }
		return h[r];
	}
    public static ArrayList<ArrayList <Integer>> GetGraph(int n,int m){
        ArrayList<ArrayList <Integer>> a=new ArrayList<>();
        for(int i=0;i<n;i++){
            a.add(new ArrayList<>());
        }
        for(int i=0;i<m;i++){
            int u=sc.nextInt()-1;
            int v=sc.nextInt()-1;
            a.get(u).add(v);
            a.get(v).add(u);
        } 
        return a;
    }
    
   
    
    public static void main(String[] args) {
        // code starts..
        int n=sc.nextInt();
        ArrayList<ArrayList<Integer>> a=GetGraph(n, n-1);
        int h[]=new int[n];int p[]=new int[n];int vis[]=new int[n];
        
        pw.println(hieght(0, new double[n], a, vis, p));
    
        // Code ends...
        pw.flush();
        pw.close();
    }
    public static Comparator<Integer> C(){
        return 
        new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return o2.compareTo(o1);//for descending
            }
        };
    }
    public static Comparator<Pair> di(){
        return 
        new Comparator<Pair>() {
            @Override
            public int compare(Pair o1, Pair o2) {
                Long a=o1.j;
                Long b=o2.j;
                return a.compareTo(b);//ascending
            }
        };
    }
    static class tripletL implements Comparable<tripletL> {
        Long x, y, z;
 
        tripletL(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }
 
        public int compareTo(tripletL o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);
 
            return result;
        }
 
        public boolean equlas(Object o) {
            if (o instanceof tripletL) {
                tripletL p = (tripletL) o;
                return (x - p.x == 0) && (y - p.y ==0 ) && (z - p.z == 0);
            }
            return false;
        }
 
        public String toString() {
            return x + " " + y + " " + z;
        }
 
        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }
    public static String Doubleformate(double a,int n){
        String s="";
        while(n-->0){
            s+='0';
        }
        DecimalFormat f =new DecimalFormat("#0."+s);
        return f.format(a);
    }
 
    public static Comparator<Integer[]> column(int i){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
                return o1[i].compareTo(o2[i]);//for ascending
                //return o2[i].compareTo(o1[i]);//for descending
            }
        };
    }
    public static Comparator<Long[]> column1(int i){
        return 
        new Comparator<Long[]>() {
            @Override
            public int compare(Long[] o1, Long[] o2) {
                return o1[i].compareTo(o2[i]);//for ascending
                //return o2[i].compareTo(o1[i]);//for descending
            }
        };
    }
    public static Comparator<Integer[]> pair(){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
                int result=o1[0].compareTo(o2[0]);
                if(result==0)
                result=o1[1].compareTo(o2[1]);
                return result;
            }
        };
    }
    public static Comparator<Integer[]> Triplet(){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
            
                    for(int i=0;i<3;i++){
                        for(int j=i+1;j<3;j++){
                            for(int k=0;k<3;k++){
                                for(int p=k+1;p<3;p++){
                                    if((o1[i]==o2[k]&&o1[j]==o2[p])||(o1[j]==o2[k]&&o1[i]==o2[p])){
 
                                    }
                                }
                            }
                        }
                    }
                    int result=o1[0].compareTo(o2[0]);
                    if(result==0)
                    result=o1[1].compareTo(o2[1]);
                    if(result==0)
                    result=o1[2].compareTo(o2[2]);
                    return result;
            }
        };
    }
    
    
    public static String reverseString(String s){
        StringBuilder input1 = new StringBuilder(); 
        input1.append(s);  
        input1 = input1.reverse();
        return input1.toString();
    }
    public static int[] scanArray(int n){
        int a[]=new int [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextInt();
 
        return a;
    }
    public static long[] scanLongArray(int n){
        long a[]=new long [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextLong();
 
        return a;
    }
    public static String [] scanStrings(int n){
        String a[]=new String [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextLine();
 
        return a;
    }
     
}
class Pair{
    int i;
    long j;
    Pair(int a,long b){
        i=a;
        j=b;
    }
}
class InputReader {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }