Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
G = [[] for _ in range(N+1)]
for i in range(N-1):
    a, b = map(int, input().split())
    G[a].append((b, i))
    G[b].append((a, i))


def get_path(u, v):
    stack = [u]
    prev = [None] * (N+1)
    visited = [False] * (N+1)
    visited[u] = True
    while stack:
        node = stack.pop()
        for next, i in G[node]:
            if not visited[next]:
                visited[next] = True
                prev[next] = (node, i)
                stack.append(next)
    path = 0
    node = v
    while node != u:
        p, i = prev[node]
        node = p
        path += 1 << i
    return path


def count(bits, N):
    cnt = 0
    for i in range(N):
        if ((bits >> i) & 1) == 1:
            cnt += 1
    return cnt


M = int(input())
uv = [tuple(map(int, input().split())) for _ in range(M)]
paths = [get_path(u, v) for u, v in uv]
ans = 2**(N-1)
for bit in range(1, 1 << M):
    cnt = 0
    tmp = 0
    for i in range(M):
        if ((bit >> i) & 1) == 1:
            cnt += 1
            tmp |= paths[i]
    ans += (-1)**cnt * 2**(N-1-count(tmp, N-1))
print(ans)


Fixed submission:
import sys
input = sys.stdin.readline

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


def get_path(u, v):
    stack = [u]
    prev = [None] * (N+1)
    visited = [False] * (N+1)
    visited[u] = True
    while stack:
        node = stack.pop()
        for next, i in G[node]:
            if not visited[next]:
                visited[next] = True
                prev[next] = (node, i)
                stack.append(next)
    path = 0
    node = v
    while node != u:
        p, i = prev[node]
        node = p
        path += 1 << i
    return path


def count(bits, N):
    cnt = 0
    for i in range(N):
        if ((bits >> i) & 1) == 1:
            cnt += 1
    return cnt


M = int(input())
uv = [tuple(map(int, input().split())) for _ in range(M)]
paths = [get_path(u, v) for u, v in uv]
ans = 2**(N-1)
for bit in range(1, 1 << M):
    cnt = 0
    tmp = 0
    for i in range(M):
        if ((bit >> i) & 1) == 1:
            cnt += 1
            tmp |= paths[i]
    ans += (-1)**cnt * 2**(N-1-count(tmp, N-1))
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
G = [[] for _ in range(N+1)]
for _ in range(N-1):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)


def get_path(u, v):
    stack = [u]
    prev = [-1] * (N+1)
    visited = [False] * (N+1)
    visited[u] = True
    while stack:
        node = stack.pop()
        for next in G[node]:
            if not visited[next]:
                visited[next] = True
                prev[next] = node
                stack.append(next)
    path = [v]
    node = v
    while node != u:
        p = prev[node]
        path.append(p)
        node = p
    return path[::-1]


def get_size(paths):
    edges = set()
    for path in paths:
        for i in range(len(path)-1):
            u = path[i]
            v = path[i+1]
            if u > v:
                u, v = v, u
            edges.add((u, v))
    return len(edges)


M = int(input())
uv = [tuple(map(int, input().split())) for _ in range(M)]
paths = [get_path(u, v) for u, v in uv]
ans = 2**(N-1)
for bit in range(1, 1 << M):
    cnt = 0
    tmp = []
    for i in range(M):
        if ((bit >> i) & 1) == 1:
            cnt += 1
            tmp.append(paths[i])
    x = get_size(tmp)
    ans += (-1)**cnt * 2**(N-1-get_size(tmp))
print(ans)


Fixed submission:
import sys
input = sys.stdin.readline

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


def get_path(u, v):
    stack = [u]
    prev = [None] * (N+1)
    visited = [False] * (N+1)
    visited[u] = True
    while stack:
        node = stack.pop()
        for next, i in G[node]:
            if not visited[next]:
                visited[next] = True
                prev[next] = (node, i)
                stack.append(next)
    path = 0
    node = v
    while node != u:
        p, i = prev[node]
        node = p
        path += 1 << i
    return path


def count(bits, N):
    cnt = 0
    for i in range(N):
        if ((bits >> i) & 1) == 1:
            cnt += 1
    return cnt


M = int(input())
uv = [tuple(map(int, input().split())) for _ in range(M)]
paths = [get_path(u, v) for u, v in uv]
ans = 2**(N-1)
for bit in range(1, 1 << M):
    cnt = 0
    tmp = 0
    for i in range(M):
        if ((bit >> i) & 1) == 1:
            cnt += 1
            tmp |= paths[i]
    ans += (-1)**cnt * 2**(N-1-count(tmp, N-1))
print(ans)