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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    G = [[] for _ in range(N)]
    for i in range(N - 1):
        a,b = map(int,input().split())
        a -= 1
        b -= 1
        G[a].append((b,i))
        G[b].append((a,i))
    
    between = [[set() for _ in range(N)] for _ in range(N)]
    for i in range(N):
        stack = [(i,[])]
        while stack:
            v,before = stack.pop()
            between[i][v] = set(before)
            for e,j in G[v]:
                if e == i or len(between[i][e]) >= 1:
                    continue
                between[i][e] = set(before + [j])
                stack.append((e,before + [j]))
            #print('before: ',before)
            #print('v :',v)
    
    #print(between)

    M = int(input())
    condition = [tuple(map(int,input().split())) for _ in range(M)]
    condition = [(a - 1,b - 1) for a,b in condition]
    
    ans = 0
    for bit in range(1<<M):
        ret = set()
        cnt = 0
        for i in range(M):
            if (bit>>i)&1:
                cnt += 1
                ret |= between[condition[i][0]][condition[i][1]]
        
        free = N - len(ret) - 1
        #print('free :',free)
        if cnt%2 == 0:
            ans += pow(2,free)
        else:
            ans -= pow(2,free)
    print(ans)
if __name__ == '__main__':
    main()