Buggy python submission (verdict: Time Limit Exceeded):
from functools import lru_cache

N = int(input())

adj = [list() for _ in range(N)]
for _ in range(N-1):
    a,b = map(int,input().split())
    adj[a-1].append(b-1)
    adj[b-1].append(a-1)

parent = [None]*N
visited = [False]*N
visited[0] = True
def rec(u):
    for v in adj[u]:
        if not visited[v]:
            parent[v] = u
            visited[v] = True
            rec(v)
rec(0)
del adj

M = int(input())


# edge_id to crucial query_id
tasks = [set() for _ in range(N)]

for q in range(M):
    u,v = map(int,input().split())
    u,v = u-1,v-1
    u2r = []
    v2r = []
    while u is not None:
        u2r.append(u)
        u = parent[u]
    while v is not None:
        v2r.append(v)
        v = parent[v]
    
    for i,(a,b) in enumerate(zip(reversed(u2r), reversed(v2r))):
        if a != b:
            break
    else:
        i += 1
    # path = u2r[:-i] + [u2r[-i]] + list(reversed(v2r[:-i]))

    for n in u2r[:-i]:
        tasks[n].add(q)
    for n in v2r[:-i]:
        tasks[n].add(q)

tasks = tasks[1:]

@lru_cache(None)
def rec(i, remainings):
    if i >= len(tasks):
        return 1 if not remainings else 0
    r = remainings & tasks[i]
    if not r:
        return 2*rec(i+1,remainings)

    #True
    return rec(i+1, remainings) + rec(i+1, frozenset(remainings-tasks[i]))

print(rec(0, frozenset(range(M))))

Fixed submission:
from itertools import combinations

N = int(input())

adj = [list() for _ in range(N)]
for _ in range(N-1):
    a,b = map(int,input().split())
    adj[a-1].append(b-1)
    adj[b-1].append(a-1)

parent = [None]*N
visited = [False]*N
visited[0] = True
def rec(u):
    for v in adj[u]:
        if not visited[v]:
            parent[v] = u
            visited[v] = True
            rec(v)
rec(0)
del adj

M = int(input())


# edge_id to crucial query_id
tasks = []

for q in range(M):
    u,v = map(int,input().split())
    u,v = u-1,v-1
    u2r = []
    v2r = []
    while u is not None:
        u2r.append(u)
        u = parent[u]
    while v is not None:
        v2r.append(v)
        v = parent[v]
    
    for i,(a,b) in enumerate(zip(reversed(u2r), reversed(v2r))):
        if a != b:
            break
    else:
        i += 1
    # path = u2r[:-i] + [u2r[-i]] + list(reversed(v2r[:-i]))
    tasks.append(u2r[:-i]+v2r[:-i])

cnt = 0
sign = 1

for n in range(1,M+1):
    sub = 0
    for p in combinations(range(M),n):
        sub += 2**(N-1-len(set().union(*(tasks[i] for i in p))))
    cnt += sign*sub
    sign *= -1
print(2**(N-1)-cnt)

Buggy python submission (verdict: Time Limit Exceeded):
from functools import lru_cache

N = int(input())

adj = [list() for _ in range(N)]
for _ in range(N-1):
    a,b = map(int,input().split())
    adj[a-1].append(b-1)
    adj[b-1].append(a-1)

parent = [None]*N
visited = [False]*N
visited[0] = True
def rec(u):
    for v in adj[u]:
        if not visited[v]:
            parent[v] = u
            visited[v] = True
            rec(v)
rec(0)
del adj

M = int(input())


# edge_id to crucial query_id
tasks = [set() for _ in range(N)]

for q in range(M):
    u,v = map(int,input().split())
    u,v = u-1,v-1
    u2r = []
    v2r = []
    while u is not None:
        u2r.append(u)
        u = parent[u]
    while v is not None:
        v2r.append(v)
        v = parent[v]
    
    for i,(a,b) in enumerate(zip(reversed(u2r), reversed(v2r))):
        if a != b:
            break
    else:
        i += 1
    # path = u2r[:-i] + [u2r[-i]] + list(reversed(v2r[:-i]))

    for n in u2r[:-i]:
        tasks[n].add(q)
    for n in v2r[:-i]:
        tasks[n].add(q)

tasks = tasks[1:]

@lru_cache(None)
def rec(i, remainings):
    if i >= len(tasks):
        return 1 if not remainings else 0
    r = remainings & tasks[i]
    if not r:
        return 2*rec(i+1,remainings)

    #True
    return rec(i+1, remainings) + rec(i+1, frozenset(remainings-tasks[i]))

print(rec(0, frozenset(range(M))))

Fixed submission:
from itertools import combinations

N = int(input())

adj = [list() for _ in range(N)]
for _ in range(N-1):
    a,b = map(int,input().split())
    adj[a-1].append(b-1)
    adj[b-1].append(a-1)

parent = [None]*N
visited = [False]*N
visited[0] = True
def rec(u):
    for v in adj[u]:
        if not visited[v]:
            parent[v] = u
            visited[v] = True
            rec(v)
rec(0)
del adj

M = int(input())


# edge_id to crucial query_id
tasks = []

for q in range(M):
    u,v = map(int,input().split())
    u,v = u-1,v-1
    u2r = []
    v2r = []
    while u is not None:
        u2r.append(u)
        u = parent[u]
    while v is not None:
        v2r.append(v)
        v = parent[v]
    
    for i,(a,b) in enumerate(zip(reversed(u2r), reversed(v2r))):
        if a != b:
            break
    else:
        i += 1
    # path = u2r[:-i] + [u2r[-i]] + list(reversed(v2r[:-i]))
    tasks.append(u2r[:-i]+v2r[:-i])

cnt = 0
sign = 1

for n in range(1,M+1):
    sub = 0
    for p in combinations(range(M),n):
        sub += 2**(N-1-len(set().union(*(tasks[i] for i in p))))
    cnt += sign*sub
    sign *= -1
print(2**(N-1)-cnt)