Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i.

Consider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the following M restrictions?

The i-th (1 \leq i \leq M) restriction is represented by two integers u_i and v_i, which mean that the path connecting Vertex u_i and Vertex v_i must contain at least one edge painted black.

Constraints

2 \leq N \leq 50

1 \leq a_i,b_i \leq N

The graph given in input is a tree.

1 \leq M \leq \min(20,\frac{N(N-1)}{2})

1 \leq u_i < v_i \leq N

If i \not= j, either u_i \not=u_j or v_i\not=v_j

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}
M
u_1 v_1
:
u_M v_M

Output

Print the number of ways to paint the edges that satisfy all of the M conditions.

Sample Input 1

3
1 2
2 3
1
1 3

Sample Output 1

3

The tree in this input is shown below:

All of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.

Sample Input 2

2
1 2
1
1 2

Sample Output 2

1

The tree in this input is shown below:

All of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.

Sample Input 3

5
1 2
3 2
3 4
5 3
3
1 3
2 4
2 5

Sample Output 3

9

The tree in this input is shown below:

Sample Input 4

8
1 2
2 3
4 3
2 5
6 3
6 7
8 6
5
2 7
3 5
1 6
2 8
7 8

Sample Output 4

62

The tree in this input is shown below:

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Queue;
import java.util.LinkedList;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FTreeAndConstraints solver = new FTreeAndConstraints();
        solver.solve(1, in, out);
        out.close();
    }

    static class FTreeAndConstraints {
        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int n = s.nextInt();
            int[][][] used = new int[n][n][n - 1];
            int[] a = new int[n - 1];
            int[] b = new int[n - 1];
            ArrayList<Integer>[] adj = new ArrayList[n];
            for (int i = 0; i < n; i++)
                adj[i] = new ArrayList<>();
            for (int i = 0; i < n - 1; i++) {
                a[i] = s.nextInt() - 1;
                b[i] = s.nextInt() - 1;
                adj[a[i]].add(b[i]);
                adj[b[i]].add(a[i]);
            }
            for (int i = 0; i < n - 1; i++) {
                ArrayList<Integer> A = new ArrayList<>();
                int[] vis = new int[n];
                Queue<Integer> q = new LinkedList<>();
                q.add(a[i]);
                A.add(a[i]);
                vis[a[i]] = 1;
                while (!q.isEmpty()) {
                    int x = q.poll();
                    for (int y : adj[x]) {
                        if (y != b[i] && vis[y] == 0) {
                            vis[y] = 1;
                            q.add(y);
                            A.add(y);
                        }
                    }
                }
                ArrayList<Integer> B = new ArrayList<>();
                q.add(b[i]);
                B.add(b[i]);
                vis[b[i]] = 1;
                while (!q.isEmpty()) {
                    int x = q.poll();
                    for (int y : adj[x]) {
                        if (y != a[i] && vis[y] == 0) {
                            vis[y] = 1;
                            q.add(y);
                            B.add(y);
                        }
                    }
                }
                for (int u : A) {
                    for (int v : B) {
                        used[u][v][i] = 1;
                        used[v][u][i] = 1;
                    }
                }
            }
            int m = s.nextInt();
            int[] u = new int[m];
            int[] v = new int[m];
            for (int i = 0; i < m; i++) {
                u[i] = s.nextInt() - 1;
                v[i] = s.nextInt() - 1;
            }
            long res = 0;
            for (int i = 0; i < (1 << m); i++) {
                int[] x = new int[n - 1];
                int temp = i;
                int c = 0, set = 0;
                while (temp > 0) {
                    if ((temp & 1) == 1) {
                        for (int j = 0; j < n - 1; j++)
                            x[j] |= used[u[c]][v[c]][j];
                        set ^= 1;
                    }
                    c++;
                    temp = temp >> 1;
                }
                int edges = 0;
                for (int j = 0; j < n - 1; j++)
                    edges += x[j];
                if ((set & 1) == 0)
                    res += 1L << (n - 1 - edges);
                else
                    res -= 1L << (n - 1 - edges);
            }
            w.println(res);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(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 nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int 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 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;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}