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.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {

    private static final int MOD = (int)1e9 + 7; //998244353;
    private static final long INF = (long)1e15;

    private List<Integer>[] adj;
    private int[] sum;
    private int[] A, B;

    public Main(FastScanner in, PrintWriter out) {
        int N = in.nextInt();

        adj = new List[N];
        for (int i = 0; i < N; i++)
            adj[i] = new ArrayList<>();

        for (int i = 1; i < N; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            adj[u].add(v);
            adj[v].add(u);
        }


        int M = in.nextInt();
        A = new int[M];
        B = new int[M];
        for (int i = 0; i < M; i++) {
            A[i] = in.nextInt() - 1;
            B[i] = in.nextInt() - 1;
        }

        long ans = 1L << (N - 1);
        LCA lca = new LCA(N, adj);
        sum = new int[N];
        for (int i = 1; i < 1 << M; i++) {
            Arrays.fill(sum, 0);
            for (int j = 0; j < M; j++) if (((1 << j) & i) != 0) {
                int a = A[j], b = B[j];
                int p = lca.query(a, b);
                // sum[i] is the number starting vertex for a path in the
                // subtree of i (including i)
                sum[a] += 1;
                sum[b] += 1;
                // the path won't go above lca, so we substract the number of
                // nodes here. So from lca, all sum[i] is 0.
                // sum[i] is 0 means the edge from i going back to root is not
                // on any valid path.
                sum[p] -= 2;
            }
            // use dfs to count how many edges are required to connect
            // all nodes in the current selected vertex set
            int cnt = dfs(0, -1);
            long cur = 1L << (N - 1 - cnt);
            // inclusion/exclusion principle
            if (Integer.bitCount(i) % 2 == 1) ans -= cur;
            else ans += cur;
        }
        out.println(ans);
    }

    private int dfs(int u, int p) {
        int res = 0;
        for (int v : adj[u]) {
            if (v == p) continue;
            res += dfs(v, u);
            sum[u] += sum[v];
        }
        if (sum[u] > 0) res++;
        return res;
    }

    private int gcd(int a, int b) {
        while (true) {
            if (b == 0) return a;
            int tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    private long gcd(long a, long b) {
        while (true) {
            if (b == 0) return a;
            long tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    private long powm(long x, long p) {
        long res = 1;
        while (p > 0) {
            if (p % 2 == 1)
                res = res * x % MOD;
            x = x * x % MOD;
            p /= 2;
        }
        return res;
    }

    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        // Scanner in = new Scanner(
                // new BufferedReader(new InputStreamReader(System.in)));
        FastScanner in = new FastScanner(System.in);

        Main sol = new Main(in, out);
        out.close();
    }
}

class LCA {
    private int D;
    private int[] depth;
    private int[][] par;

    public LCA(int n, List<Integer>[] adj) {
        D = Integer.numberOfTrailingZeros(Integer.highestOneBit(n));
        par = new int[D + 1][n];
        for (int[] pp : par)
            Arrays.fill(pp, -1);

        depth = new int[n];

        boolean[] seen = new boolean[n];
        Queue<Integer> q = new ArrayDeque<>();
        seen[0] = true;
        q.add(0);

        while (!q.isEmpty()) {
            int u = q.remove();
            for (int v : adj[u]) {
                if (seen[v]) continue;
                q.add(v);
                seen[v] = true;
                depth[v] = depth[u] + 1;
                par[0][v] = u;
            }
        }

        for (int d = 1; d <= D; d++) {
            for (int i = 0; i < n; i++) {
                int mid = par[d - 1][i];
                if (mid >= 0)
                    par[d][i] = par[d - 1][mid];
            }
        }
    }

    private int walk(int u, int k) {
        for (int d = 0; d <= D; d++) if (((1 << d) & k) != 0) {
            u = par[d][u];
        }
        return u;
    }

    public int query(int u, int v) {
        if (depth[u] < depth[v])
            v = walk(v, depth[v] - depth[u]);
        else if (depth[u] > depth[v])
            u = walk(u, depth[u] - depth[v]);
        if (u == v)
            return u;
        // find u, v such that par[0][u] == par[0][v]
        for (int d = D; d >= 0; d--) {
            // if par[d][u] == par[d][v], the jump is too big
            if (par[d][u] != par[d][v]) {
                u = par[d][u];
                v = par[d][v];
            }
        }
        return par[0][u];
    }
}

// Pair
class Pair<T extends Comparable<? super T>, U extends Comparable<? super U>> implements Comparable<Pair<T, U>> {
    T a;
    U b;
    Pair() { }
    Pair(T a, U b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public String toString() { return "("+a.toString()+", "+b.toString()+")"; }

    @Override
    public int hashCode() { return Objects.hash(a, b); }

    @Override
    public boolean equals(Object obj) {
        if(this == obj) return true;
        if(obj == null) return false;
        if(this.getClass() != obj.getClass()) return false;
        Pair that = (Pair) obj;
        if(this.a.getClass() != that.a.getClass()) return false;
        if(this.b.getClass() != that.b.getClass()) return false;
        if(!this.a.equals(that.a)) return false;
        if(!this.b.equals(that.b)) return false;
        return true;
    }

    @Override
    public int compareTo(Pair<T, U> that) {
        int c = (this.a).compareTo(that.a);
        if(c == 0) c = (this.b).compareTo(that.b);
        return c;
    }
}


class FastScanner{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream)
    {
        this.stream = stream;
    }

    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++];
    }

    boolean isSpaceChar(int c)
    {
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }

    boolean isEndline(int c)
    {
        return c=='\n'||c=='\r'||c==-1;
    }

    int nextInt()
    {
        return Integer.parseInt(next());
    }

    long nextLong()
    {
        return Long.parseLong(next());
    }

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

    String next(){
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isSpaceChar(c));
        return res.toString();
    }

    String nextLine(){
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isEndline(c));
        return res.toString();
    }
}