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.*;
import java.util.*;

class Edge{
	int id, to;

	public Edge(int id, int to) {
		super();
		this.id = id;
		this.to = to;
	}
	
}

public class Main {
	static int n;
	static List<Edge> g[];
	static int m;
	static int a[][];
	static long memo[];
	static void solve() {
		n = ni();
		g = new ArrayList[n];
		for(int i=0;i<n;i++)g[i] = new ArrayList<>();
		for(int i=0;i<n-1;i++) {
			int a = ni()-1, b = ni()-1;
			g[a].add(new Edge(i, b));
			g[b].add(new Edge(i, a));
		}
		m = ni();
		a = new int[m][2];
		memo = new long[m];//longのbitでエッジが含まれるか否かを表現する
		for(int i=0;i<m;i++) {
			int u = ni()-1 , v = ni()-1;
			dfs(u, -1, v, i);
		}
		long ans = 0;
		for(int i=1;i<1<<m;i++) {
			long vs = 0;
			int bitCount = Integer.bitCount(i);
			for(int j=0;j<m;j++) {
				if((i>>j&1)==1) {
					vs |= memo[j];
				}
			}
			long t = pow(2, n - 1 - Long.bitCount(vs));
			if(bitCount%2==1) ans += t;
			else ans -= t;
		}
		ans = pow(2, n-1) - ans;
		out.println(ans);
	}
	
	static boolean dfs(int u, int p, int v,  int idx) {
		if(u == v) {
			return true;
		}
		boolean isPath = false;
		for(Edge e:g[u]) {
			if(e.to == p)continue;
			if(dfs(e.to, u, v, idx)) {
				memo[idx] |= 1L << e.id;
				isPath = true;
			}
		}
		return isPath;
	}

	//constant
	static final long mod = Long.MAX_VALUE;
	static final int dx[] = { -1, 0, 1, 0 }, dy[] = { 0, -1, 0, 1 };
	static final int[] dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final int inf = Integer.MAX_VALUE / 2;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final double eps = 1e-10;
	static final double pi = Math.PI;
	static StringBuilder sb = new StringBuilder();
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	//libraries
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(char ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static String getReverse(String s) {
		char c[] = s.toCharArray();
		reverse(c);
		s = String.valueOf(c);
		return s;
	}

	static <T> void reverse(List<T> ls) {
		int sz = ls.size();
		for (int i = 0; i < sz / 2; i++) {
			T t = ls.get(i);
			ls.set(i, ls.get(sz - 1 - i));
			ls.set(sz - 1 - i, t);
		}
	}

	static <T> void reverse(T[] ar) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			T t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void sbnl() {//StringBuilderに改行文字をappendする
		sb.append("\n");
	}

	static int lowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static <T> int lowerBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int upperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rupperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rlowerBound(List<T> ls, T x) {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static double max(double x, double y) {
		return Math.max(x, y);
	}

	static double min(double x, double y) {
		return Math.min(x, y);
	}

	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static void sort(int[] ar) {
		Arrays.sort(ar);
	}

	static void sort(long[] ar) {
		Arrays.sort(ar);
	}

	static void sort(double[] ar) {
		Arrays.sort(ar);
	}

	static void sort(char[] ar) {
		Arrays.sort(ar);
	}

	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(char[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}

	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}

	static void fill(boolean arr[], boolean x) {
		Arrays.fill(arr, x);
	}

	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}

	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(boolean arr[][], boolean x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}

	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}

	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	//input
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;

	private static int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}

	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}

	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	@SuppressWarnings("unused")
	private static long[] nla(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	@SuppressWarnings("unused")
	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

}