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.text.DecimalFormat;

/**
 *
 * @author HulkBuster
 * 
 */
public class CF839C {
public static int mod = (int) (1e9 + 7);
public static InputReader in;
public static PrintWriter out;

public static void solve() throws FileNotFoundException {

	in = new InputReader(System.in);
	out = new PrintWriter(System.out);
	int n = in.ni();
	ArrayList<Integer>gr[]=new ArrayList[n+1];
	Queue<Integer>q=new LinkedList<>();
	int level[]=new int[n+1];
	double pro[] = new double[n+1];
	HashSet<Integer>pe = new HashSet<>();
	for(int i =1;i<=n;i++){
		gr[i]=new ArrayList<>();
		level[i] = -1;
	}
	for(int i =1;i<n;i++){
		int a = in.ni();
		int b=in.ni();
		
		gr[a].add(b);
		gr[b].add(a);
	}
	for(int i=2;i<=n;i++){
		if(gr[i].size()<2)
			pe.add(i);
	}
	level[1]=0;
	pro[1] = 1;
	q.add(1);
	while(!q.isEmpty()){
		
		int pr = q.poll();
		int cc=0;
		
		for (Iterator iterator = gr[pr].iterator(); iterator.hasNext();){
			Integer integer = (Integer) iterator.next();
			if(level[integer]==-1)
				cc++;
		}
		double p = pro[pr]/(double)cc;
		for (Iterator iterator = gr[pr].iterator(); iterator.hasNext();) {
			Integer integer = (Integer) iterator.next();
			if(level[integer]==-1){
				level[integer]=1+level[pr];
				q.add(integer);
				pro[integer] = p;
			}
		}
	}
	double ex =0;
	for (Iterator iterator = pe.iterator(); iterator.hasNext();) {
		Integer integer = (Integer) iterator.next();
		ex = ex + (double)level[integer]*pro[integer];
		//out.println(integer);
	}
	
	DecimalFormat df = new DecimalFormat("#0.000000000000000");
	out.println(df.format(ex));
	out.close();
}

public static void main(String[] args) {
	new Thread(null, new Runnable() {
		public void run() {
			try {
				solve();
			} catch (Exception e) {
				e.printStackTrace();
			}
		}
	}, "1", 1 << 26).start();
}

static class Pair implements Comparable<Pair> {

	int x, y, i;

	Pair(int x, int y, int i) {
		this.x = x;
		this.y = y;
		this.i = i;
	}

	Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}

	public int compareTo(Pair o) {
		if (this.x != o.x)
			return Integer.compare(this.x, o.x);
		else
			return Integer.compare(this.y, o.y);
		//return 0;
	}

	public boolean equals(Object o) {
		if (o instanceof Pair) {
			Pair p = (Pair) o;
			return p.x == x && p.y == y && p.i == i;
		}
		return false;
	}

	public int hashCode() {
		return new Integer(x).hashCode() * 31 + new Integer(y).hashCode() + new Integer(i).hashCode() * 37;
	}

}

public static long add(long a, long b) {
	long x = (a + b);
	while (x >= mod)
		x -= mod;
	return x;
}

public static long sub(long a, long b) {
	long x = (a - b);
	while (x < 0)
		x += mod;
	return x;
}

public static long mul(long a, long b) {
	long x = (a * b);
	while (x >= mod)
		x -= mod;
	return x;
}

public static boolean isPal(String s) {
	for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
		if (s.charAt(i) != s.charAt(j))
			return false;
	}
	return true;
}

public static String rev(String s) {
	StringBuilder sb = new StringBuilder(s);
	sb.reverse();
	return sb.toString();
}

public static long gcd(long x, long y) {
	if (x % y == 0)
		return y;
	else
		return gcd(y, x % y);
}

public static int gcd(int x, int y) {
	if (x % y == 0)
		return y;
	else
		return gcd(y, x % y);
}

public static long gcdExtended(long a, long b, long[] x) {

	if (a == 0) {
		x[0] = 0;
		x[1] = 1;
		return b;
	}
	long[] y = new long[2];
	long gcd = gcdExtended(b % a, a, y);

	x[0] = y[1] - (b / a) * y[0];
	x[1] = y[0];

	return gcd;
}

public static long mulmod(long a, long b, long m) {
	if (m <= 1000000009)
		return a * b % m;

	long res = 0;
	while (a > 0) {
		if ((a & 1) != 0) {
			res += b;
			if (res >= m)
				res -= m;
		}
		a >>= 1;
		b <<= 1;
		if (b >= m)
			b -= m;
	}
	return res;
}

public static int abs(int a, int b) {
	return (int) Math.abs(a - b);
}

public static long abs(long a, long b) {
	return (long) Math.abs(a - b);
}

public static int max(int a, int b) {
	if (a > b)
		return a;
	else
		return b;
}

public static int min(int a, int b) {
	if (a > b)
		return b;
	else
		return a;
}

public static long max(long a, long b) {
	if (a > b)
		return a;
	else
		return b;
}

public static long min(long a, long b) {
	if (a > b)
		return b;
	else
		return a;
}

public static long pow(long n, long p, long m) {
	long result = 1;
	if (p == 0)
		return 1;
	if (p == 1)
		return n;
	while (p != 0) {
		if (p % 2 == 1)
			result *= n;
		if (result >= m)
			result %= m;
		p >>= 1;
		n *= n;
		if (n >= m)
			n %= m;
	}
	return result;
}

public static long pow(long n, long p) {
	long result = 1;
	if (p == 0)
		return 1;
	if (p == 1)
		return n;
	while (p != 0) {
		if (p % 2 == 1)
			result *= n;
		p >>= 1;
		n *= n;
	}
	return result;
}

public static void debug(Object... o) {
	System.out.println(Arrays.deepToString(o));
}

static 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 ni() {
		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 nl() {
		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[] nIArr(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = ni();
		}
		return a;
	}

	public long[] nLArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = nl();
		}
		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);
	}

}
}