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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

#region いつもの
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static Global;
using static NumGlobal;

static class Global
{
    public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value);
    public static T[] NewArray<T>(int len0, Func<T> factory)
    {
        var arr = new T[len0];
        for (int i = 0; i < arr.Length; i++) arr[i] = factory();
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value);
        return arr;
    }
    public static T[][] NewArray<T>(int len0, int len1, Func<T> factory)
    {
        var arr = new T[len0][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value);
        return arr;
    }
    public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory)
    {
        var arr = new T[len0][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value);
        return arr;
    }
    public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory)
    {
        var arr = new T[len0][][][];
        for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory);
        return arr;
    }
    private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
    public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
    public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
}
static class NumGlobal
{
    public static int Pow(int x, int y)
    {
        int res = 1;
        for (; y > 0; y >>= 1)
        {
            if ((y & 1) == 1) res *= x;
            x *= x;
        }
        return res;
    }
    public static BigInteger ParseBigInteger(string s)
    {
        // MonoのBigInteger.Parseが遅いので自前実装
        var res = BigInteger.Zero;
        var splited = new string[(s.Length + 7) / 8];
        for (var i = 0; i < splited.Length - 1; i++)
        {
            splited[i] = s.Substring(8 * i, 8);
        }
        splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
        foreach (var sp in splited)
        {
            res *= (int)Math.Pow(10, sp.Length);
            res += int.Parse(sp);
        }
        return res;
    }
    public static int BitCount(int x) { x -= (x >> 1) & 0x55555555; x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x + (x >> 4)) & 0x0f0f0f0f; x += x >> 8; x += x >> 16; return x & 0x3f; }
    public static int BitCount(long x) { x -= (x >> 1) & 0x5555555555555555; x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x += x >> 8; x += x >> 16; x += x >> 32; return (int)(x & 0x0000007f); }
    public static int MSB(int x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return BitCount(x) - 1; }
    public static int MSB(long x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; x |= x >> 32; return BitCount(x) - 1; }
    public static int LSB(int x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; return 32 - BitCount(x); }
    public static int LSB(long x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; x |= x << 32; return 64 - BitCount(x); }
}
static class Ext
{
    public static T[] Fill<T>(this T[] arr, T value)
    {
        for (var i = 0; i < arr.Length; i++) arr[i] = value;
        return arr;
    }
    public static T[] Sort<T>(this T[] arr)
    {
        Array.Sort(arr);
        return arr;
    }
    public static string[] Sort(this string[] arr)
    {
        Array.Sort(arr, StringComparer.OrdinalIgnoreCase);
        return arr;
    }
    public static T[] Reverse<T>(this T[] arr)
    {
        Array.Reverse(arr);
        return arr;
    }

    public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
        (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
        where TMax : IComparable<TMax>
    {
        TMax max;
        TSource maxByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        maxByItem = e.Current;
        max = maxBySelector(maxByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = maxBySelector(item);
            if (max.CompareTo(next) < 0)
            {
                max = next;
                maxByItem = item;
            }
        }
        return Tuple.Create(maxByItem, max);
    }
    public static Tuple<TSource, TMin> MinBy<TSource, TMin>
        (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
        where TMin : IComparable<TMin>
    {
        TMin min;
        TSource minByItem;

        var e = source.GetEnumerator();
        e.MoveNext();
        minByItem = e.Current;
        min = minBySelector(minByItem);
        while (e.MoveNext())
        {
            var item = e.Current;
            var next = minBySelector(item);
            if (min.CompareTo(next) > 0)
            {
                min = next;
                minByItem = item;
            }
        }
        return Tuple.Create(minByItem, min);
    }
    public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
    public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
    public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
}
#pragma warning disable CA1819
[System.Diagnostics.DebuggerNonUserCode]
public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String { get; } } public SplitLine Split => new SplitLine(this); public class RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (int i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public string[] String => this.Select(cr => cr.String); public int[] Int => this.Select(cr => cr.Int); public int[] Int0 => this.Select(cr => cr.Int - 1); public long[] Long => this.Select(cr => cr.Long); public double[] Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
public class Program
{
    [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;

    public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
    static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

    #endregion
    public object Calc()
    {
        var N = cr.Int;

        var edges = new Dictionary<int, int>();
        var gb = new GraphBuilder(N, false);
        for (var i = 0; i < N - 1; i++)
        {
            var l = cr.Int0;
            var r = cr.Int0;
            edges[l * 100 + r] = edges[l + r * 100] = i;
            gb.Add(l, r);
        }
        var tree = gb.ToTree(0);
        var M = cr.Int;
        var constraints = cr.Repeat(M).Select(cr => Tuple.Create(cr.Int0, cr.Int0));

        var lcaBuilder = new LowestCommonAncestor(tree);
        var lca = NewArray(N, N, 0);
        for (int i = 0; i < N; i++)
            for (int j = i; j < N; j++)
                lca[i][j] = lca[j][i] = lcaBuilder.Lca(i, j);
        var routes = NewArray(N, N, 0L);
        for (int i = 0; i < N; i++)
            for (int j = i + 1; j < N; j++)
            {
                var l = lca[i][j];
                long b = 0;
                var node = tree[i];
                while (node.index != l)
                {
                    b |= 1L << edges[node.index + node.root * 100];
                    node = tree[node.root];
                }
                node = tree[j];
                while (node.index != l)
                {
                    b |= 1L << edges[node.index + node.root * 100];
                    node = tree[node.root];
                }

                routes[i][j] = routes[j][i] = b;
            }
        long res = 0;
        var M2 = 1 << M;
        for (int i = 1; i < M2; i++)
        {
            long b = 0;
            for (int x = i, ci = 0; x > 0; x >>= 1, ci++)
                if ((x & 1) == 1)
                    b |= routes[constraints[ci].Item1][constraints[ci].Item2];

            long cnt = 1L << (N - BitCount(b) - 1);
            if (BitCount(i) % 2 == 0)
                res -= cnt;
            else
                res += cnt;
        }

        return (1L << (N - 1)) - res;
    }
}
class GraphBuilder
{
    private List<int>[] roots;
    private List<int>[] children;
    public GraphBuilder(int count, bool isOriented = true)
    {
        this.roots = new List<int>[count];
        this.children = new List<int>[count];
        for (var i = 0; i < count; i++)
        {
            if (isOriented)
            {
                this.roots[i] = new List<int>();
                this.children[i] = new List<int>();
            }
            else
            {
                this.roots[i] = this.children[i] = new List<int>();
            }
        }
    }
    public GraphBuilder(int count, ConsoleReader cr, int edgeCount, bool isOriented = true) : this(count, isOriented)
    {
        for (var i = 0; i < edgeCount; i++)
            this.Add(cr.Int - 1, cr.Int - 1);
    }
    public void Add(int from, int to)
    {
        children[from].Add(to);
        roots[to].Add(from);
    }
    public TreeNode[] ToTree(int root)
    {
        if (this.roots[0] != this.children[0]) throw new Exception("木には無向グラフをしたほうが良い");
        var res = new TreeNode[this.children.Length];
        res[root] = new TreeNode(root, -1, 0, this.children[root].ToArray());

        var queue = new Queue<int>();
        foreach (var child in res[root].children)
        {
            res[child] = new TreeNode(child, root, 1, Array.Empty<int>());
            queue.Enqueue(child);
        }

        while (queue.Count > 0)
        {
            var from = queue.Dequeue();
            if (res[from].root == -1)
                res[from].children = this.children[from].ToArray();
            else
            {
                var children = new List<int>(this.children[from].Count);
                foreach (var c in this.children[from])
                    if (c != res[from].root)
                        children.Add(c);

                res[from].children = children.ToArray();
            }

            foreach (var child in res[from].children)
            {
                res[child] = new TreeNode(child, from, res[from].depth + 1, Array.Empty<int>());
                queue.Enqueue(child);
            }
        }

        return res;
    }

    public Node[] ToArray() =>
        Enumerable
        .Zip(roots, children, (r, c) => Tuple.Create(r, c))
        .Select((t, i) => new Node(i, t.Item1.ToArray(), t.Item2.ToArray()))
        .ToArray();
}
class TreeNode : IEquatable<TreeNode>
{
    public TreeNode(int i, int root, int depth, int[] children)
    {
        this.index = i;
        this.root = root;
        this.children = children;
        this.depth = depth;
    }
    public int index;
    public int root;
    public int depth;
    public int[] children;

    public override string ToString() => $"children: {string.Join(",", children)}";
    public override bool Equals(object obj)
    {
        if (obj is TreeNode)
            return this.Equals((TreeNode)obj);
        else
            return false;
    }
    public bool Equals(TreeNode other) => this.index == other.index;
    public override int GetHashCode() => this.index;
}
class Node : IEquatable<Node>
{
    public Node(int i, int[] roots, int[] children)
    {
        this.index = i;
        this.roots = roots;
        this.children = children;
    }
    public int index;
    public int[] roots;
    public int[] children;

    public override string ToString() => $"children: {string.Join(",", children)}";
    public override bool Equals(object obj)
    {
        if (obj is Node)
            return this.Equals((Node)obj);
        else
            return false;
    }
    public bool Equals(Node other) => this.index == other.index;
    public override int GetHashCode() => this.index;
}

class LowestCommonAncestor // 最小共通祖先
{
    private TreeNode[] tree;

    // kprv[u,k] 頂点uの2^k個上の祖先頂点v, 0<=k<logN
    private int[,] kprv;
    private int logN;
    public LowestCommonAncestor(TreeNode[] tree)
    {
        if (tree.Length == 0) throw new ArgumentException(nameof(tree));

        this.tree = tree;
        this.logN = (int)(Math.Log(tree.Length, 2) + 1);
        this.kprv = new int[tree.Length, logN];
        for (int v = 0; v < tree.Length; v++)
        {
            this.kprv[v, 0] = tree[v].root;
        }
        for (int k = 0; k < logN - 1; k++)
        {
            for (int v = 0; v < tree.Length; v++)
            {
                if (this.kprv[v, k] < 0)
                    this.kprv[v, k + 1] = -1;
                else
                    this.kprv[v, k + 1] = this.kprv[this.kprv[v, k], k];
            }
        }
    }

    public int Lca(int u, int v)
    {
        if (Depth(u) > Depth(v))
        {
            var tmp = u;
            u = v;
            v = tmp;
        }
        for (int k = 0; k <= logN; k++)
        {
            if ((((Depth(v) - Depth(u)) >> k) & 1) == 1)
            {
                v = kprv[v, k];
            }
        }
        if (u == v)
            return u;

        for (int k = logN - 1; k >= 0; k--)
        {
            if (kprv[u, k] != kprv[v, k] && kprv[u, k] != -1 && kprv[v, k] != -1)
            {
                u = kprv[u, k];
                v = kprv[v, k];
            }
        }
        return kprv[u, 0];
    }

    int Depth(int index) => tree[index].depth;
}