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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;

public class C {
	public static void main(String[] args) {
		List<String> input = getRawInput();
		// # of nodes in the graph
		int n = Integer.parseInt(input.get(0).trim());
							
		if (n >= 2) {
			int m[][] = getMatrix(n, input);
						
			Map<Integer, Node> map = new HashMap<>();
			int root = 1;
			Node rootNode = new Node(root);
			rootNode.setDistance(0);			
			map.put(1, rootNode);

			
			Graph graph = new Graph(rootNode);
			List<Node> nodes = new ArrayList<Node>();
			
			for (int i = 2; i <= n; i++) {
				Node node = new Node(i);
				nodes.add(node);
				map.put(i, node);	
			}
						
			for (int i=0;i<input.size()-1;i++) {									
				map.get(m[i][0]).addNeighbour(map.get(m[i][1]));
				map.get(m[i][1]).addNeighbour(map.get(m[i][0]));							
			}
			
			
			
			for (int k=1;k<=n;k++) {				
				Node current = map.get(k);
				graph.addNode(current);
			}
			
			// BFS uses a queue - set the distance and the probability to get at the desired point
			bfs(graph);
			
			
			
										
//			for (int k=1;k<=n;k++) {				
//				Node current = map.get(k);
//				System.out.println("value: "+current.getValue()+"  neighbours: "+current.getNeighbour().size() 
//						+"distance "+current.getDistance()+"  prob: "+current.getProbabiliy()+ " leaf: "+current.getLeaf());				
//			}
			
			double result =0;
			for (int k=1;k<=n;k++) {				
				Node current = map.get(k);
				if (current.getLeaf()) {
					result+=current.getDistance()*current.getProbabiliy();
				}
			}
			
			System.out.println(result);
			
			
			
			
										
		} else if (n == 1) {
			System.out.println("0");			
		}

	
	}

	private static void bfs(Graph graph) {
		
		Node s = graph.getRoot();		
		Queue<Node> qe=new LinkedList<Node>();
		
		s.setVisited(true);
		s.setProbabiliy(1);
		qe.add(s);
		
		while (!qe.isEmpty()) {					
			Node c = qe.poll();
			//System.out.println("current node extracted :"+c.getValue());
			List<Node> neighbours = c.getNeighbour();
			
			double n = neighbours.size();
			if (n==1) {
				c.setAsLeaf();
			}
			
			int unvisited = 0;
			for (int i=0;i<n;i++) {
				if (!neighbours.get(i).getVisited()) {
					unvisited++;
				}
			}			
			double probability  = c.getProbabiliy()/unvisited;			
			int distance = c.getDistance()+1;
						
			for (int i=0;i<neighbours.size();i++) {				
				Node t = neighbours.get(i);
				if (!t.getVisited()) {
					t.setDistance(distance);
					t.setProbabiliy(probability);
					t.setVisited(true);
					qe.add(t);
				}
			}
			
		}
		
	}

	private static int[][] getMatrix(int n, List<String> input) {
		int result[][] = new int[n-1][2];
		for (int i=1;i<input.size();i++) {
			result[i-1][0] = Integer.parseInt(input.get(i).trim().split(" ")[0]);
			result[i-1][1] = Integer.parseInt(input.get(i).trim().split(" ")[1]);
		}		
		return result;
	}

	public static List<String> getRawInput() {
		List<String> line = new ArrayList<>();

		try {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			String fl = br.readLine().trim();
			String[] firstLine = fl.split(" ");
			line.add(fl);
			int k = 0;
			while (k < Integer.parseInt(firstLine[0]) - 1 && line.add(br.readLine().trim())
					&& !line.get(line.size() - 1).trim().equals("")) {
				k++;
			}
		} catch (IOException e) {
			e.printStackTrace();
		}
		return line;

	}

}

class Graph {
	
	
	
	private Node root;
	private List<Node> nodes = new ArrayList<>();
	
	public Graph(Node root) {		
		this.root = root;	
		nodes.add(root);
	}

	public Node getRoot() {		
		return this.root;
	}

	public void addNode(Node current) {
		nodes.add(current);		
	}
}

class Node {
	// list of neighbours for one node
	private List<Node> neighbours = new ArrayList<>();

	// value of the node
	private int value;

	// flag if visited
	private boolean visited = false;

	// probability to get
	private double probabiliy;
	
	// from the root
	private int distance;
	
	// true if it is leafe
	private boolean leafe = false;
	
	public Node(int value) {
		this.value = value;
	}
	
	public void setAsLeaf() {
		this.leafe = true;
	}
	
	public boolean getLeaf() {
		return this.leafe;
	}
	
	
	public void setDistance(int distance) {
		this.distance=distance;	
	}
	
	public int getDistance () {
		return this.distance;
	}

	public int getValue() {
		return this.value;
	}

	public void addNeighbour(final Node child) {
		neighbours.add(child);
	}
	
	public List<Node> getNeighbour() {
		return neighbours;
	}

	public boolean getVisited() {
		return visited;
	}

	public void setVisited(boolean b) {
		this.visited = b;
	}

	public double getProbabiliy() {
		return probabiliy;
	}

	public void setProbabiliy(double probability) {
		this.probabiliy = probability;
	}

}