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

//•*¨*•.¸¸♪I/O•*¨*•.¸¸♪

var (
	sc = bufio.NewScanner(os.Stdin)
	wr = bufio.NewWriter(os.Stdout)
)

func scanInt() int {
	sc.Scan()
	a,_ := strconv.Atoi(sc.Text())
	return a
}

func scanInt64() int64 {
	sc.Scan()
	a,_ := strconv.ParseInt(sc.Text(),10,64)
	return a
}

func scanFloat64() float64 {
	sc.Scan()
	a,_ := strconv.Atoi(sc.Text())
	return float64(a)
}

func scanInts(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ { res[i] = scanInt() }
	return res
}

func scanText() string {
	sc.Scan()
	return sc.Text()
}

func printInts(a ...int) {
	for i, e := range a {
		fmt.Fprint(wr, e)
		if i != len(a)-1 { fmt.Fprint(wr, " ") }
	}
	fmt.Fprintln(wr)
	wr.Flush()
}

//•*¨*•.¸¸♪Main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)

func main() {
	sc.Split(bufio.ScanWords)
	// sc.Buffer(make([]byte, 10000), 100000000)

	n := scanInt()

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

	for i := 0; i < n-1; i++ {
		a,b := scanInt()-1, scanInt()-1
		g[a] = append(g[a],b)
		g[b] = append(g[b],a)
	}

	edge := make([]int64, n)
	done := make([]bool, n)
	q := make([]int, 0)
	q = append(q, 0)
	done[0] = true

	for len(q)!=0 {
		next := q[0]
		for _, e := range g[next] {
			if done[e] {
				continue
			}

			edge[e] = int64(1<<uint(e-1)) | edge[next]
			q = append(q, e)
			done[e] = true
		}
		q = q[1:]
	}

	m := scanInt()
	path := make([]int64, m)

	for i := 0; i < m; i++ {
		v,u := scanInt()-1, scanInt()-1
		path[i] = edge[u]^edge[v]
	}

	ans := int64(0)

	for i := 0; i < (1<<uint(m)); i++ {
		sign := 1
		p := int64(0)
		for j := 0; j < m; j++ {
			if i>>uint(j)&1 == 1 {
				p |= path[j]
				sign *= -1
			}
		}

		cnt := 0
		for j := 0; j < n-1; j++ {
			if p>>uint(j)&1==1 {
				cnt++
			}
		}

		ans += int64(sign)*int64(1<<uint(n-1-cnt))
	}

	fmt.Println(ans)
}