Problem: 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.

Examples

Input

3
1 2
2 3
1
1 3


Output

3


Input

2
1 2
1
1 2


Output

1


Input

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


Output

9


Input

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


Output

62

Solution (in JAVA):

Solution:
import java.util.BitSet;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        final int N = sc.nextInt();
        int[][] paths = new int[N - 1][2];
        for (int i = 0; i < paths.length; i++) {
            sc.nextLine();
            int a = sc.nextInt();
            int b = sc.nextInt();
            paths[i][0] = Math.min(a, b);
            paths[i][1] = Math.max(a, b);
        }

        sc.nextLine();
        final int M = sc.nextInt();
        BitSet[] constraints = new BitSet[M];
        for (int i = 0; i < M; i++) {
            sc.nextLine();
            int u = sc.nextInt();
            int v = sc.nextInt();
            BitSet constraint = new BitSet(paths.length);
            travel(constraint, paths, u, v);
            constraints[i] = constraint;
        }
        //        for (int i = 0; i < paths.length; i++) {
        //            System.out.println(i + ": " + paths[i][0] + " -> " + paths[i][1]);
        //        }
        //        for (BitSet constraint : constraints) {
        //            System.out.println(constraint);
        //        }

        long finalResult = 0;
        for (int i = 0; i < (int) Math.pow(2, M); i++) {
            BitSet result = new BitSet(paths.length);
            int orCount = 0;
            for (int j = 0; j < M; j++) {
                if (((1 << j) & i) == (1 << j)) {
                    result.or(constraints[j]);
                    orCount++;
                }
            }
            long tmpResult = (long) Math.pow(2, N - 1 - result.cardinality());
            //System.out.println(result + ":" + tmpResult);
            if (orCount % 2 == 0) {
                finalResult += tmpResult;
            } else {
                finalResult -= tmpResult;
            }
        }
        System.out.println(finalResult);
    }

    static boolean travel(BitSet constraint, int[][] paths, int from, int to) {
        int tmp = Math.min(from, to);
        to = Math.max(from, to);
        from = tmp;
        for (int i = 0; i < paths.length; i++) {
            if (constraint.get(i)) {
                continue;
            }
            int[] path = paths[i];
            if (path[0] == from && path[1] == to) {
                constraint.set(i);
                return true;
            } else if (path[0] == from) {
                constraint.set(i);
                if (travel(constraint, paths, path[1], to)) {
                    return true;
                }
                constraint.set(i, false);
            } else if (path[1] == from) {
                constraint.set(i);
                if (travel(constraint, paths, to, path[0])) {
                    return true;
                }
                constraint.set(i, false);
            }
        }
        return false;
    }
}