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:
	        			/*
	        		     * Author- Priyam Vora
	        		     * BTech 2nd Year DAIICT
	        		     */
	     
	     
	        		    import java.awt.Checkbox;
	import java.awt.Point;
	import java.io.*;
	        		    import java.math.*;
	        		    import java.util.*;
	import java.util.Map.Entry;
	
	import javax.print.attribute.SetOfIntegerSyntax;
	
	     
	        		    public class Main{
	        		  	private static InputStream stream;
	        		    	private static byte[] buf = new byte[1024];
	        		    	private static int curChar;
	        		    	private static int numChars;
	        		    	private static SpaceCharFilter filter;
	        		    	private static PrintWriter pw;
	        		    	private static long count = 0,mod=1000000007;
	        		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
	        		    	public final static int INF = (int) 1E9;
	
	        		        public static void main(String args[]) {
	        		        	InputReader(System.in);
	        		    		pw = new PrintWriter(System.out); 
	        		            new Thread(null ,new Runnable(){
	        		               public void run(){
	        		                   try{
	        		                       solve();
	        		                       pw.close();
	        		                   } catch(Exception e){
	        		                       e.printStackTrace();
	        		                   }
	        		               }
	        		           },"1",1<<26).start();
	        		       }
	        		        static StringBuilder sb;
	        		        public static void test(){
	        		        	 sb=new StringBuilder();
	        		        	int t=nextInt();
	        		        	while(t-->0){
	        		        		solve();
	        		        	}
	        		        	pw.println(sb);
	        		        }
	        		        public static long pow(long n, long p,long mod) {
	        					if(p==0)
	        						return 1;
	        					if(p==1)
	        						return n%mod;
	        					if(p%2==0){
	        						long temp=pow(n, p/2,mod);
	        					return (temp*temp)%mod;
	        					}else{
	        						 	long temp=pow(n,p/2,mod);
	        						 	temp=(temp*temp)%mod;
	        						 	return(temp*n)%mod;
	        						 	
	        					}
	        				}
	        		        public static long pow(long n, long p) {
	        					if(p==0)
	        						return 1;
	        					if(p==1)
	        						return n;
	        					if(p%2==0){
	        						long temp=pow(n, p/2);
	        					return (temp*temp);
	        					}else{
	        						 	long temp=pow(n,p/2);
	        						 	temp=(temp*temp);
	        						 	return(temp*n);
	        						 	
	        					}
	        				}
	        		        public static void Merge(long a[],int p,int r){
	        		            if(p<r){
	        		                int q = (p+r)/2;
	        		                Merge(a,p,q);
	        		                Merge(a,q+1,r);
	        		                Merge_Array(a,p,q,r);
	        		            }
	        		        }
	        		        public static void Merge_Array(long a[],int p,int q,int r){
	        		           long b[] = new long[q-p+1];
	        		            long c[] = new long[r-q];
	        		            for(int i=0;i<b.length;i++)
	        		                b[i] = a[p+i];
	        		            for(int i=0;i<c.length;i++)
	        		                c[i] = a[q+i+1];
	        		            int i = 0,j = 0;
	        		            for(int k=p;k<=r;k++){
	        		                if(i==b.length){
	        		                    a[k] = c[j];
	        		                    j++;
	        		                }
	        		                else if(j==c.length){
	        		                    a[k] = b[i];
	        		                    i++;
	        		                }
	        		                else if(b[i]<c[j]){
	        		                    a[k] = b[i];
	        		                    i++;
	        		                }
	        		                else{
	        		                    a[k] = c[j];
	        		                    j++;
	        		                }
	        		            }
	        		        }
	        		    	public static long gcd(long x, long y) {
	        		    		if (x == 0)
	        		    			return y;
	        		    		else
	        		    			return gcd( y % x,x);
	        		    	}	public static boolean isPrime(int n) {
	        		    	// Corner cases
				    		if (n <= 1)
				    			return false;
				    		if (n <= 3)
				    			return true;
				     
				    		// This is checked so that we can skip 
				    		// middle five numbers in below loop
				    		if (n % 2 == 0 || n % 3 == 0)
				    			return false;
				     
				    		for (int i = 5; i * i <= n; i = i + 6)
				    			if (n % i == 0 || n % (i + 2) == 0)
				    				return false;
				     
				    		return true;
				    	}
	        		        static LinkedList<Integer> adj[];
	        		        static boolean Visited[];
	        		        static HashSet<Integer> exc;
	        		        static long oddsum[]=new long[1000001];
	        		        static int co=0,ans=0;
	        		    
	        		     
	        		      
	        		       
	        		        static int[] levl;
	        		        static int[] no;
	        		        private static void solve(){
	        		    		int n=nextInt();
	        		    		LinkedList<Integer>[] l=new LinkedList[n];
	        		    		for(int i=0;i<n;i++)
	        		    			l[i]=new LinkedList<>();
	        		    		for(int i=0;i<n-1;i++){
	        		    			int u=nextInt()-1;
	        		    			int v=nextInt()-1;
	        		    			l[u].add(0,v);
	        		    			l[v].add(0,u);
	        		    		}
	        		    		pw.printf("%.15f",dfs(l,0,-1));
	        		    	}
	        		    	
	        		    	private static double dfs(LinkedList<Integer>[] graph,int cur,int prev){
	        		    		double ret=0;
	        		    		double num=0;
	        		    		Iterator<Integer> it=graph[cur].listIterator();
	        		    		while(it.hasNext()){
	        		    			int x=it.next();
	        		    			if(x!=prev){
	        		    				ret+=(1+dfs(graph,x,cur));
	        		    				num++;
	        		    			}
	        		    		}
	        		    		if(num!=0){
	        		    			ret=ret/num;
	        		    		}
	        		    		return ret;
	        		    	}
	        		       
	        		        public static String reverseString(String s) {
	        					StringBuilder sb = new StringBuilder(s);
	        					sb.reverse();
	        					return (sb.toString());
	        				}
	        		        
	        		        
	        		       private static void BFS(int sou){
	        		        	Queue<Integer> q=new LinkedList<Integer>();
	        		        	q.add(sou);
	        		        	Visited[sou]=true;
	        		        	levl[sou]=0;
	        		        	while(!q.isEmpty()){
	        		        		int top=q.poll();
	        		        		
	        		        		for(int i:adj[top]){
	        		        			//pw.println(i+" "+top);
	        		        			if(!Visited[i])
	        		        			{
	        		        				
	        		        				q.add(i);
	        		        				levl[i]=levl[top]+1;
	        		        			}
	        		        			
	        		        			Visited[i]=true;
	        		        			
	        		        			}
	        		        		}
	        		        	}
	        		        	
	        		        
	        		        private static long ncr(int n,int k){
	    				    	if (k < 0 || k > n) return 0;
	    				        if (n-k < k) k = n-k;
	    			
	    				        BigInteger x = BigInteger.ONE;
	    				        for (int i = 1; i <= k; i++) {
	    				            x = x.multiply(new BigInteger(""+(n-i+1)));
	    				            x = x.divide(new BigInteger(""+i));
	    				        }
	    			
	    				return x.longValue();
	    				    }
	        		       private  static long fact(long count){
	        		        	long ans=1;
	        		        	for(int i=1;i<=count;i++){
	        		        		ans*=i;
	        		        	}
	        		        	return ans;
	        		        }
	        		        
	        		        
	        		        static int state=1;
	        		        static long no_exc=0,no_vert=0;
	        		      static Stack<Integer> st;
	        		      static HashSet<Integer> inset;
	        		        private static void topo(int curr){
	        		        	
	        		        	Visited[curr]=true;
	        		        	inset.add(curr);
	        		        	for(int x:adj[curr]){
	        		        		if(adj[x].contains(curr) || inset.contains(x)){
	        		        			state=0;
	        		        			return;
	        		        		}
	        		        		if(state==0)
	        		        			return;
	        		        		
	        		        	}
	        		        	st.push(curr);
	        		        	
	        		        	inset.remove(curr);
	        		        }
	        		        static HashSet<Integer> hs;
	        		       
	        		     	private static void buildgraph(int n){
	        		    		adj=new LinkedList[n+1];
	        		    		Visited=new boolean[n+1];
	        		    		levl=new int[n+1];
	        		    		no=new int[n+1];
	        		    		for(int i=0;i<=n;i++){
	        		    			adj[i]=new LinkedList<Integer>();
	        		    		
	        		    		}
	     
	     
	        		    	}
	        		     	
	        		    	// To Get Input
	        		    	// Some Buffer Methods
	     
	        		     	public static void sort(long a[]){
	        		     		Merge(a, 0, a.length-1);
	        		     	}
	        		    	public static void InputReader(InputStream stream1) {
	        		    		stream = stream1;
	        		    	}
	     
	        		    	private static boolean isWhitespace(int c) {
	        		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	        		    	}
	     
	        		    	private static boolean isEndOfLine(int c) {
	        		    		return c == '\n' || c == '\r' || c == -1;
	        		    	}
	     
	        		    	private static int read() {
	        		    		if (numChars == -1)
	        		    			throw new InputMismatchException();
	        		    		if (curChar >= numChars) {
	        		    			curChar = 0;
	        		    			try {
	        		    				numChars = stream.read(buf);
	        		    			} catch (IOException e) {
	        		    				throw new InputMismatchException();
	        		    			}
	        		    			if (numChars <= 0)
	        		    				return -1;
	        		    		}
	        		    		return buf[curChar++];
	        		    	}
	     
	        		    	private static int nextInt() {
	        		    		int c = read();
	        		    		while (isSpaceChar(c))
	        		    			c = read();
	        		    		int sgn = 1;
	        		    		if (c == '-') {
	        		    			sgn = -1;
	        		    			c = read();
	        		    		}
	        		    		int res = 0;
	        		    		do {
	        		    			if (c < '0' || c > '9')
	        		    				throw new InputMismatchException();
	        		    			res *= 10;
	        		    			res += c - '0';
	        		    			c = read();
	        		    		} while (!isSpaceChar(c));
	        		    		return res * sgn;
	        		    	}
	     
	        		    	private static long nextLong() {
	        		    		int c = read();
	        		    		while (isSpaceChar(c))
	        		    			c = read();
	        		    		int sgn = 1;
	        		    		if (c == '-') {
	        		    			sgn = -1;
	        		    			c = read();
	        		    		}
	        		    		long res = 0;
	        		    		do {
	        		    			if (c < '0' || c > '9')
	        		    				throw new InputMismatchException();
	        		    			res *= 10;
	        		    			res += c - '0';
	        		    			c = read();
	        		    		} while (!isSpaceChar(c));
	        		    		return res * sgn;
	        		    	}
	     
	        		    	private static String nextToken() {
	        		    		int c = read();
	        		    		while (isSpaceChar(c))
	        		    			c = read();
	        		    		StringBuilder res = new StringBuilder();
	        		    		do {
	        		    			res.appendCodePoint(c);
	        		    			c = read();
	        		    		} while (!isSpaceChar(c));
	        		    		return res.toString();
	        		    	}
	     
	        		    	private static String nextLine() {
	        		    		int c = read();
	        		    		while (isSpaceChar(c))
	        		    			c = read();
	        		    		StringBuilder res = new StringBuilder();
	        		    		do {
	        		    			res.appendCodePoint(c);
	        		    			c = read();
	        		    		} while (!isEndOfLine(c));
	        		    		return res.toString();
	        		    	}
	     
	        		    	private static int[] nextIntArray(int n) {
	        		    		int[] arr = new int[n];
	        		    		for (int i = 0; i < n; i++) {
	        		    			arr[i] = nextInt();
	        		    		}
	        		    		return arr;
	        		    	}
	     
	        		    	private static long[][] next2dArray(int n, int m) {
	        		    		long[][] arr = new long[n][m];
	        		    		for (int i = 0; i < n; i++) {
	        		    			for (int j = 0; j < m; j++) {
	        		    				arr[i][j] = nextLong();
	        		    			}
	        		    		}
	        		    		return arr;
	        		    	}
	        		    	private static char[][] nextCharArray(int n,int m){
	        		    		char [][]c=new char[n][m];
	        		    		for(int i=0;i<n;i++){
	        		    			String s=nextLine();
	        		    			for(int j=0;j<s.length();j++){
	        		    				c[i][j]=s.charAt(j);
	        		    			}
	        		    		}
	        		    		return c;
	        		    	}
	     
	        		    	private static long[] nextLongArray(int n) {
	        		    		long[] arr = new long[n];
	        		    		for (int i = 0; i < n; i++) {
	        		    			arr[i] = nextLong();
	        		    		}
	        		    		return arr;
	        		    	}
	     
	        		    	private static void pArray(int[] arr) {
	        		    		for (int i = 0; i < arr.length; i++) {
	        		    			pw.print(arr[i] + " ");
	        		    		}
	        		    		pw.println();
	        		    		return;
	        		    	}
	     
	        		    	private static void pArray(long[] arr) {
	        		    		for (int i = 0; i < arr.length; i++) {
	        		    			pw.print(arr[i] + " ");
	        		    		}
	        		    		pw.println();
	        		    		return;
	        		    	}
	     
	        		    	private static void pArray(boolean[] arr) {
	        		    		for (int i = 0; i < arr.length; i++) {
	        		    			pw.print(arr[i] + " ");
	        		    		}
	        		    		pw.println();
	        		    		return;
	        		    	}
	     
	        		    	private static boolean isSpaceChar(int c) {
	        		    		if (filter != null)
	        		    			return filter.isSpaceChar(c);
	        		    		return isWhitespace(c);
	        		    	}
	     
	        		    	private interface SpaceCharFilter {
	        		    		public boolean isSpaceChar(int ch);
	        		    	}
	        		    	
	        		    	private static void merge_sort(int a[],int p,int q){
	        		    		if(p>q)
	        		    			return;
	        		    		int mid=(p+q)/2;
	        		    		int l[]=new int[mid];
	        		    		int r[]=new int[a.length - mid];
	        		    		for(int i=0;i<mid;i++){
	        		    			l[i]=a[i];
	        		    		}
	        		    		for(int i=mid;i<a.length;i++)
	        		    			r[i]=a[i];
	        		    		merge_sort(l,p,mid);
	        		    		merge_sort(r,mid+1,q);
	        		    		merge(l,r,a);
	        		    	}
	        		    	private static void merge(int l[],int r[],int a[]){
	        		    		int i=0,j=0,k=0;
	        		    		int nl=l.length;
	        		    		int nr=r.length;
	        		    		while(i<nl && j<nr){
	        		    			if(l[i]<r[j]){
	        		    				a[k]=l[i];
	        		    				k++;
	        		    				i++;  
	        		    			}else {
	        		    				a[k]=r[j];
	        		    				k++;
	        		    				j++;
	        		    			}
	        		    				
	        		    			}
	        		    		while(i<nl){
	        		    			a[k]=l[i];
	        		    			i++;
	        		    			k++;
	        		    		}
	        		    		while(j<nr){
	        		    			a[k]=r[j];
	        		    			j++;
	        		    			k++;
	        		    		}
	        		    	}
	     
	     
	    }
	        		    
	        		           		    class Node{
	        		    	int to;
	        		    	long dist;
	        		    	Node(int to,long dist){
	        		    		this.to=to;
	        		    		this.dist=dist;
	        		    	}
	        		    	
	        		    }
	        		   /* class Pair implements Comparable<Pair>{
	        				
	    					
	    					int ele,ind;
	    					Pair(int ele,int ind){
	    					
	    						this.ele=ele;
	    						this.ind=ind;
	    					
	    					}
	    					@Override
	    					public int compareTo(Pair o) {
	    				
	    							
	    							return ele-o.ele;
	    					}
	    					public int hashCode() {
	    							//int hu = (int) (x ^ (x >>> 32));
	    							//int hv = (int) (y ^ (y >>> 32));
	    							//int hw = (int) (mass ^ (mass >>> 32));
	    							//return 31 * hu + hv ;
	    						return 0;
	    						}
	    						public boolean equals(Object o) {
	    							Pair other = (Pair) o;
	    						//	return x == other.x && y == other.y;
	    						return false;
	    						}
	    				}  */class Dsu{
		    		    	private int rank[], parent[] ,n;
		    		    	private static int[] parent1;
		    		    	Dsu(int size){
		    		    		this.n=size+1;
		    		    		rank=new int[n];
		    		    		//parent=new int[n];
		    		    		parent=new int[n];
		    		    	makeSet();
		    		
		    		    	}
		    		    	
		    		    	void makeSet(){
		    		    		for(int i=0;i<n;i++){
		    		    			parent[i]=i;
		    		    		}
		    		    	}
		    		    	
		    		    	int find(int x){
		    		    		if(parent[x]!=x){
		    		    			
		    		    			parent[x]=find(parent[x]);
		    		    		}
		    		    		return parent[x];
		    		    	}
		    		    
		    		    	
		    		    	boolean union(int x,int y){
		    		    		int xRoot=find(x);
		    		    		int yRoot=find(y);
		    		    		
		    		    		if(xRoot==yRoot)
		    		    			return false;
		    		    		if(rank[xRoot]<rank[yRoot]){
		    		    		parent[xRoot]=yRoot;	
		    		    		}else if(rank[yRoot]<rank[xRoot]){
		    		    			parent[yRoot]=xRoot;
		    		    		}else{
		    		    			parent[yRoot]=xRoot;
		    		    			rank[xRoot]++;
		    		    		}
		    		    		return true;
		    		    	}
	
		    		     
		    		    }