Buggy python submission (verdict: Time Limit Exceeded):
#!/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

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
    for k in range(2**m):
        # Fill black
        dp[i][k | status] += dp[i-1][k]
        # Fill white
        dp[i][k] += dp[i-1][k]

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

Fixed submission:
#!/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]
    return False
 
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)]
# White
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
 
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
    for k in range(2**m):
        # Fill black
        dp[i][k | status] += dp[i-1][k]
        # Fill white
        dp[i][k] += dp[i-1][k]
 
print(dp[-1][-1])