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 (2.4.0) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline

n = int(input())
edge = [[] for _ in range(n)]
edge_dict = dict()
edges = []

for i in range(n - 1):
    a, b = [int(item) - 1 for item in input().split()]
    edge[a].append(b)
    edge[b].append(a)
    if a > b:
        edge_dict[(b, a)] = i
        edges.append((b, a))
    else:
        edge_dict[(a, b)] = i
        edges.append((a, b))

m = int(input())
uv = []
for _ in range(m):
    uv.append([int(item) - 1 for item in input().split()])

def dfs(p, v, dest):
    if v == dest:
        return [v]
    if p != -1 and len(edge[v]) == 1:
        return False
    for nv in edge[v]:
        if nv == p:
            continue
        ret = dfs(v, nv, dest)
        if ret:
            return ret + [v]

state = [set() for _ in range(m)]
for i, (u, v) in enumerate(uv):
    ret = dfs(-1, u, v)
    for uu, vv in zip(ret, ret[1:]):
        if uu > vv:
            uu, vv = vv, uu
        if (uu, vv) in edge_dict:
            state[i].add(edge_dict[(uu, vv)])

# DP[i-th item][fills uv as st]
dp = [[0] * 2**m for _ in range(n - 1)]
dp[0][0] = 1
a, b = edges[0]
status = 0
for i, st in enumerate(state):
    if 0 in st:
        status |= 1 << i
dp[0][status] = 1

seen_state = set()
seen_state.add(0)
seen_state.add(status)
for i, (a, b) in enumerate(edges):
    if i == 0:
        continue
    status = 0
    for j, st in enumerate(state):
        if i in st:
            status |= 1 << j
    to_add = set()
    for k in seen_state:
        # Fill black
        dp[i][k | status] += dp[i-1][k]
        to_add.add(k | status)
        # Fill white
        dp[i][k] += dp[i-1][k]
    seen_state.update(to_add)

print(dp[-1][-1])