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.util.*;

public class CF_839C {
    private InputReader in;
    private PrintWriter out;
    private StringBuilder sb;
    private boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;
    private List<Integer>[] graph;
    private boolean[] visited;
    private int n;
    private double proba[];
    private int level[];
    private double ans;

    private CF_839C() throws Exception {
        long s = System.currentTimeMillis();
        init();
        solve();
        if (!onlineJudge)
            sb.append(sb.charAt(sb.length() - 1) == '\n' ? "" : '\n').append("[OK in : ").append(System.currentTimeMillis() - s).append(" ms]");
        out.print(sb);
        out.close();
    }

    public static void main(String args[]) throws Exception {
        new CF_839C();
    }

    private void init() throws Exception {
        in = new InputReader(onlineJudge ? System.in : new FileInputStream(new File("in.txt")));
        out = new PrintWriter(System.out);
        sb = new StringBuilder();
    }

    private void solve() throws Exception {
        n = in.nextInt();
        graph = new List[n + 1];
        visited = new boolean[n + 1];
        level = new int[n + 1];
        proba = new double[n + 1];
        for (int i = 1; i <= n; i++) {
            graph[i] = new ArrayList<>();
        }
        for (int i = 1; i <= n - 1; i++) {
            int u = in.nextInt(), v = in.nextInt();
            graph[u].add(v);
            graph[v].add(u);
        }
        bfs();
        sb.append(String.format("%.10f", ans));

    }

    private void bfs() {
        Queue<Integer> q = new LinkedList<>();
        q.add(1);
        level[1] = 0;
        proba[1] = 1.0;
        while (!q.isEmpty()) {
            int curr = q.poll();
            if (visited[curr]) continue;
            visited[curr] = true;
            if (graph[curr].size() == 1 && curr != 1) {
                ans += proba[curr] * level[curr];
            } else {
                int countAdj = 0;
                for (int adj : graph[curr]) {
                    if (!visited[adj]) {
                        countAdj++;
                    }
                }
                for (int adj : graph[curr]) {
                    if (!visited[adj]) {
                        level[adj] = level[curr] + 1;
                        proba[adj] = proba[curr] / countAdj;
                        q.add(adj);
                    }
                }
            }
        }
    }

    class InputReader {
        private int lenbuf = 0, ptrbuf = 0;
        private InputStream in;
        private byte[] inbuf = new byte[1024];

        InputReader(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }


        long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long[][] nextLongMatrix(int n, int m) {
            long[][] map = new long[n][];
            for (int i = 0; i < n; i++) map[i] = nextLongArray(m);
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) a[i] = nextDouble();
            return a;
        }

        double[][] nextDoubleMatrix(int n, int m) {
            double[][] map = new double[n][];
            for (int i = 0; i < n; i++) map[i] = nextDoubleArray(m);
            return map;
        }

        String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        String[] nextArray(int n) {
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) arr[i] = next();
            return arr;
        }

        String[][] nextMatrix(int n, int m) {
            String[][] map = new String[n][];
            for (int i = 0; i < n; i++) map[i] = nextArray(m);
            return map;
        }

        String nextLine() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b) && b != ' ')) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        char nextChar() {
            return (char) skip();
        }

        char[] nextCharArray(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        char[][] nextCharMatrix(int n, int m) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) map[i] = nextCharArray(m);
            return map;
        }

        int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[][] nextIntMatrix(int n, int m) {
            int[][] map = new int[n][];
            for (int i = 0; i < n; i++) map[i] = nextIntArray(m);
            return map;
        }
    }
}