Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())

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

M = int(input())
uvs = [tuple(map(int, input().split())) for _ in range(M)]

masks = []
for u, v in uvs:
    u -= 1
    v -= 1
    parent = [-1] * N
    stack = [u]
    while stack:
        node = stack.pop()
        if node == v:
            break

        for next_node in adj[node]:
            if parent[node] != next_node:
                parent[next_node] = node
                stack.append(next_node)
                
    mask = 0
    node = v
    while node != u:
        next_node = parent[node]
        i = v_index[(node, next_node)]
        mask |= 1 << i
        node = next_node
    masks.append(mask)

# print(masks)

ans = 0
for bits in range(1 << (N-1)):
    for mask in masks:
        if not bits & mask:
            break
    else:
        ans += 1

print(ans)

Fixed submission:
N = int(input())

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

M = int(input())
uvs = [tuple(map(int, input().split())) for _ in range(M)]

edges = [0] * (N - 1)
for i, (u, v) in enumerate(uvs):
    u -= 1
    v -= 1
    parent = [-1] * N
    stack = [u]
    while stack:
        node = stack.pop()
        if node == v:
            break

        for next_node in adj[node]:
            if parent[node] != next_node:
                parent[next_node] = node
                stack.append(next_node)
             
    node = v
    while node != u:
        next_node = parent[node]
        index = e_index[(node, next_node)]
        edges[index] |= 1 << i
        node = next_node

dp = [0] * (1 << M)
dp[0] = 1
for e in edges:
    for i in range((1 << M) - 1, -1, -1):
        dp[i | e] += dp[i]

print(dp[-1])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())

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

M = int(input())
uvs = [tuple(map(int, input().split())) for _ in range(M)]

masks = []
for u, v in uvs:
    u -= 1
    v -= 1
    parent = [-1] * N
    stack = [u]
    while stack:
        node = stack.pop()
        if node == v:
            break

        for next_node in adj[node]:
            if parent[node] != next_node:
                parent[next_node] = node
                stack.append(next_node)
                
    mask = 0
    node = v
    while node != u:
        next_node = parent[node]
        i = v_index[(node, next_node)]
        mask |= 1 << i
        node = next_node
    masks.append(mask)

# print(masks)

ans = 0
for bits in range(1 << (N-1)):
    for mask in masks:
        if not bits & mask:
            break
    else:
        ans += 1

print(ans)

Fixed submission:
N = int(input())

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

M = int(input())
uvs = [tuple(map(int, input().split())) for _ in range(M)]

edges = [0] * (N - 1)
for i, (u, v) in enumerate(uvs):
    u -= 1
    v -= 1
    parent = [-1] * N
    stack = [u]
    while stack:
        node = stack.pop()
        if node == v:
            break

        for next_node in adj[node]:
            if parent[node] != next_node:
                parent[next_node] = node
                stack.append(next_node)
             
    node = v
    while node != u:
        next_node = parent[node]
        index = e_index[(node, next_node)]
        edges[index] |= 1 << i
        node = next_node

dp = [0] * (1 << M)
dp[0] = 1
for e in edges:
    for i in range((1 << M) - 1, -1, -1):
        dp[i | e] += dp[i]

print(dp[-1])