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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}

func getNextUint64(scanner *bufio.Scanner) uint64 {
	i, _ := strconv.ParseUint(getNextString(scanner), 10, 64)
	return i
}

func getNextFloat64(scanner *bufio.Scanner) float64 {
	i, _ := strconv.ParseFloat(getNextString(scanner), 64)
	return i
}

func main() {
	fp := os.Stdin
	wfp := os.Stdout
	cnt := 0

	if os.Getenv("MASPY") == "ますピ" {
		fp, _ = os.Open(os.Getenv("BEET_THE_HARMONY_OF_PERFECT"))
		cnt = 3
	}
	if os.Getenv("MASPYPY") == "ますピッピ" {
		wfp, _ = os.Create(os.Getenv("NGTKANA_IS_GENIUS10"))
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(wfp)
	solve(scanner, writer)
	for i := 0; i < cnt; i++ {
		fmt.Fprintln(writer, "-----------------------------------")
		solve(scanner, writer)
	}
	writer.Flush()
}

func solve(scanner *bufio.Scanner, writer *bufio.Writer) {
	n := getNextInt(scanner)

	g := make([][]Edge, n)

	for i := 0; i < n-1; i++ {
		a := getNextInt(scanner) - 1
		b := getNextInt(scanner) - 1
		g[a] = append(g[a], Edge{
			id: i,
			to: b,
		})
		g[b] = append(g[b], Edge{
			id: i,
			to: a,
		})
	}

	m := getNextInt(scanner)
	visited := make([][]int, m)
	ee := make([]int64, m)
	var ans, horobiyo int64
	for i := 0; i < m; i++ {
		u := getNextInt(scanner) - 1
		v := getNextInt(scanner) - 1

		visited[i] = make([]int, n-1)
		dfs(u, -1, v, visited[i], g)
		for j := 0; j < n-1; j++ {
			if visited[i][j] == 0 {
				continue
			}
			ee[i] |= 1 << uint(j)
		}
	}
	for i := 0; i < 1<<uint(m); i++ {
		horobiyo = 0
		c := 0
		for j := 0; j < m; j++ {
			if i>>uint(j)&1 == 0 {
				continue
			}
			horobiyo |= ee[j]
			c++
		}
		d := n - 1
		for j := 0; j < n-1; j++ {
			d -= int(horobiyo >> uint(j) & 1)
		}
		if c%2 == 0 {
			ans += 1 << uint(d)
			continue
		}
		ans -= 1 << uint(d)
	}
	fmt.Fprintln(writer, ans)
}

func dfs(i, p, v int, visited []int, g [][]Edge) int {
	if i == v {
		return 1
	}
	r := 0

	for _, e := range g[i] {
		if e.to == p {
			continue
		}
		x := dfs(e.to, i, v, visited, g)
		if x == 1 {
			visited[e.id] = 1
			r = x
		}
	}

	return r
}

// Edge ...
type Edge struct {
	to, id int
}