Given is a tree T with N vertices. The i-th edge connects Vertex A_i and B_i (1 \leq A_i,B_i \leq N).

Now, each vertex is painted black with probability 1/2 and white with probability 1/2, which is chosen independently from other vertices. Then, let S be the smallest subtree (connected subgraph) of T containing all the vertices painted black. (If no vertex is painted black, S is the empty graph.)

Let the holeyness of S be the number of white vertices contained in S. Find the expected holeyness of S.

Since the answer is a rational number, we ask you to print it \bmod 10^9+7, as described in Notes.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq A_i,B_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
A_1 B_1
:
A_{N-1} B_{N-1}


Output

Print the expected holeyness of S, \bmod 10^9+7.

Examples

Input

3
1 2
2 3


Output

125000001


Input

4
1 2
2 3
3 4


Output

375000003


Input

4
1 2
1 3
1 4


Output

250000002


Input

7
4 7
3 1
2 6
5 2
7 1
2 7


Output

570312505
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;

public class Main {
    static final class Edge {
        public final int src;
        public final int dest;
        public final long weight;
        public Edge(int src, int dest, long weight) {
            if (src < 0 || dest < 0) {
                throw new IllegalArgumentException();
            }
            this.src = src;
            this.dest = dest;
            this.weight = weight;
        }
        public Edge reverse() {
            return new Edge(dest, src, weight);
        }
        public static List<Edge> newEdges(int[] oneBasedSrc,
                                          int[] oneBasedDest,
                                          boolean directedGraph) {
            return newEdges(oneBasedSrc, oneBasedDest, null, directedGraph);
        }
        public static List<Edge> newEdges(int[] oneBasedSrc,
                                          int[] oneBasedDest,
                                          int[] weight,
                                          boolean directedGraph) {
            if (oneBasedSrc.length != oneBasedDest.length
                || (weight != null && oneBasedSrc.length != weight.length)) {
                throw new IllegalArgumentException();
            }
            List<Edge> result = new ArrayList<>(oneBasedSrc.length
                                                * (directedGraph ? 1 : 2));
            for (int i = 0; i < oneBasedDest.length; i++) {
                if (oneBasedSrc[i] <= 0 || oneBasedDest[i] <= 0) {
                    throw new IllegalArgumentException();
                }
                Edge e = new Edge(oneBasedSrc[i] - 1,
                                  oneBasedDest[i] - 1,
                                  weight == null ? 1 : weight[i]);
                result.add(e);
                if (!directedGraph) {
                    result.add(e.reverse());
                }
            }
            return result;
        }
        public static List<List<Edge>> newSrcToEdges(int vertexCount,
                                                     Collection<Edge> edges) {
            int[] edgeCount = new int[vertexCount];
            for (Edge e : edges) {
                edgeCount[e.src]++;
            }
            List<List<Edge>> result =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            for (int i = 0; i < vertexCount; i++) {
                result.set(i, new ArrayList<>(edgeCount[i]));
            }
            for (Edge e : edges) {
                result.get(e.src).add(e);
            }
            return result;
        }
    }
    static final class Mod {
        private final int mod;
        public Mod(int mod) {
            if (mod <= 0) {
                throw new IllegalArgumentException();
            }
            this.mod = mod;
        }
        public long add(long a, long b) {
            return Math.floorMod(Math.addExact(a, b), mod);
        }
        public long subtract(long a, long b) {
            return Math.floorMod(Math.subtractExact(a, b), mod);
        }
        public long multiply(long a, long b) {
            return Math.floorMod(Math.multiplyExact(a, b), mod);
        }
        public long pow(long a, long b) {
            if (b < 0) {
                throw new IllegalArgumentException();
            }
            long r = 1;
            while (b > 0) {
                if ((b & 1) == 1) {
                    r = multiply(r, a);
                }
                a = multiply(a, a);
                b >>= 1;
            }
            return r % mod;
        }
        public long inverse(long a) {
            // assert isCoprime(a, mod);
            if (a <= 0) {
                throw new IllegalArgumentException();
            }
            long b = mod;
            long u = 1;
            long v = 0;
            while (b != 0) {
                long q = a / b;
                a -= q * b;
                u -= q * v;

                long tmp = a;
                a = b;
                b = tmp;

                tmp = u;
                u = v;
                v = tmp;
            }
            return Math.floorMod(u, mod);
        }
        public long div(long a, long b) {
            return multiply(Math.floorMod(a, mod), inverse(b));
        }
    }
    static final Mod mod = new Mod(1_000_000_007);

    static int countVertexes(List<List<Edge>> srcToEdges,
                             int[] vertexCount,
                             int vertexId,
                             int parentVertexId) {
        int result = 1;
        for (Edge e : srcToEdges.get(vertexId)) {
            if (e.dest != parentVertexId) {
                result += countVertexes(srcToEdges,
                                        vertexCount,
                                        e.dest,
                                        vertexId);
            }
        }
        return vertexCount[vertexId] = result;
    }
    static long sumCases(List<List<Edge>> srcToEdges,
                         int[] vertexCount,
                         int vertexId,
                         int parentVertexId) {
        long sum = 0;
        for (Edge e : srcToEdges.get(vertexId)) {
            if (e.dest != parentVertexId) {
                sum += mod.pow(2, vertexCount[e.dest]) - 1;
            }
        }
        int n = vertexCount.length;
        if (parentVertexId != -1) {
            sum += mod.pow(2, n - vertexCount[vertexId]) - 1;
        }
        long result = mod.pow(2, n - 1) - 1 - sum;
        for (Edge e : srcToEdges.get(vertexId)) {
            if (e.dest != parentVertexId) {
                result += sumCases(srcToEdges, vertexCount, e.dest, vertexId);
            }
        }
        return result;
    }

    // https://emtubasa.hateblo.jp/entry/2019/12/30/165145
    static void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        int[][] ab = in.nextVerticalIntArrays(2, n - 1);
        int[] a = ab[0];
        int[] b = ab[1];

        List<Edge> edges = Edge.newEdges(a, b, false);
        List<List<Edge>> srcToEdges = Edge.newSrcToEdges(n, edges);

        int[] vertexCount = new int[n];
        countVertexes(srcToEdges, vertexCount, 0, -1);

        long y = sumCases(srcToEdges, vertexCount, 0, -1);
        long x = mod.pow(2, n);
        out.println(mod.div(y, x));
    }

    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }

    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;
        MyScanner(InputStream in) {
            this.in = in;
        }
        private byte readByte() {
            if (point < readLength) {
                byte result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(byte c) {
            return 33 <= c && c <= 126;
        }
        public char nextChar() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        public String next() {
            return next(16);
        }
        public String next(int n) {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        public long nextLong() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        public int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        public long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        public char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        public char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        public int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        public long[][] nextVerticalLongArrays(int arrayCount,
                                               int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        public char[][] nextVerticalCharArrays(int arrayCount,
                                               int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        public void joinAndPrintln(int[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(int[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(long[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(long[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(Iterable<?> iterable) {
            joinAndPrintln(iterable, " ");
        }
        public void joinAndPrintln(Iterable<?> iterable, String delimiter) {
            StringBuilder b = new StringBuilder();
            for (Iterator<?> i = iterable.iterator(); i.hasNext();) {
                b.append(i.next());
                while (i.hasNext()) {
                    b.append(delimiter).append(i.next());
                }
            }
            println(b.toString());
        }
    }
}
