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.math.*;
import java.io.*;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
public class Hello {

  static ArrayList<Integer> []nb = new ArrayList[200001];
  static int n;
  static int []vis = new int[100001];
  static double ans = 0;
  static void dfs(int r, double p)
  {
    ans += p;
    vis[r] = 1;
    for (int j = 0;j < nb[r].size();++j) {
      int nxt = nb[r].get(j).intValue();
      if (vis[nxt] == 0) {
	if (r == 1) {
	  dfs(nxt, p / nb[r].size());
	} else {
	  dfs(nxt, p / (nb[r].size() - 1));
	}
      }
    }
  }


  public static void main(String[] args) {
    //Scanner in = new Scanner(System.in);
    FastReader in = new FastReader(System.in);

    n = in.nextInt();
    for (int i = 1;i <= n;i++) {
      nb[i] = new ArrayList<Integer>();
    }
    for (int i = 0;i < n - 1;i++) {
      int u = in.nextInt();
      int v = in.nextInt();
      nb[u].add(v);
      nb[v].add(u);
    }
    dfs(1, 1.0);

    System.out.println(ans -1 );
  }
}

class FastReader {
    private boolean finished = false;
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(InputStream stream) {
        this.stream = stream;
    }
 
    public 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++];
    }
 
    public int peek() {
        if (numChars == -1) {
            return -1;
        }
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0) {
                return -1;
            }
        }
        return buf[curChar];
    }
 
    public 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 == ',') {
                c = read();
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public 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;
    }
 
    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
 
    public boolean isSpaceChar(int c) {
        if (filter != null) {
            return filter.isSpaceChar(c);
        }
        return isWhitespace(c);
    }
 
    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    private String readLine0() {
        StringBuilder buf = new StringBuilder();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r') {
                buf.appendCodePoint(c);
            }
            c = read();
        }
        return buf.toString();
    }
 
    public String nextLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }
 
    public String nextLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines) {
            return nextLine();
        } else {
            return readLine0();
        }
    }
 
    public BigInteger nextBigInteger() {
        try {
            return new BigInteger(nextString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }
 
    public char nextCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }
 
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') {
                return res * Math.pow(10, nextInt());
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
 
    public boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }
 
    public String next() {
        return nextString();
    }
 
    public SpaceCharFilter getFilter() {
        return filter;
    }
 
    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}