Buggy python submission (verdict: Time Limit Exceeded):
from collections import deque


def getPath(adj, start, goal):
    q = deque()
    q.appendleft((start, set()))
    while len(q):
        cur, p = q.pop()
        if cur == goal:
            return p
        for nxt, npath in adj[cur]:
            if npath in p:
                continue
            npath = p | {npath}
            q.appendleft((nxt, npath))


def main():
    N = int(input())
    adj = [set() for _ in range(N)]
    for i in range(N-1):
        a, b = map(int, input().split())
        adj[a-1].add((b-1, i))
        adj[b-1].add((a-1, i))
    M = int(input())
    dp = [{tuple(): set()} for _ in range(M+1)]
    for i in range(M):
        u, v = map(int, input().split())
        dp[i+1] = dict(dp[i])
        path = getPath(adj, u-1, v-1)
        for t in dp[i]:
            dp[i+1][t + (i, )] = dp[i+1][t] | path
    ans = 0
    for key in dp[M]:
        ans += (-1) ** len(key) * 2 ** (N - len(dp[M][key]) - 1)
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from collections import deque


def getPath(adj, start, goal):
    q = deque()
    q.appendleft((start, 0))
    while len(q):
        cur, p = q.pop()
        if cur == goal:
            return p
        for nxt, nhop in adj[cur]:
            if 2**nhop & p:
                continue
            npath = p | 2**nhop
            q.appendleft((nxt, npath))


def bitcount(x):
    return bin(x).count("1")


def main():
    N = int(input())
    adj = [set() for _ in range(N)]
    for i in range(N-1):
        a, b = map(int, input().split())
        adj[a-1].add((b-1, i))
        adj[b-1].add((a-1, i))
    M = int(input())
    dp = [0] * (2**M)
    for i in range(M):
        u, v = map(int, input().split())
        path = getPath(adj, u-1, v-1)
        for j in range(2**i):
            dp[j + 2**i] = dp[j] | path
    ans = 0
    for i in range(2**M):
        ans += (-1) ** bitcount(i) * 2 ** (N - bitcount(dp[i]) - 1)
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from collections import deque


def main():
    N = int(input())
    adj = [set() for _ in range(N)]
    for i in range(N-1):
        a, b = map(int, input().split())
        adj[a-1].add((b-1, i))
        adj[b-1].add((a-1, i))
    path = [[None] * N for _ in range(N)]
    for i in range(N):
        start = i
        q = deque()
        q.appendleft((i, set()))
        while len(q):
            cur, p = q.pop()
            for nxt, npath in adj[cur]:
                if npath in p:
                    continue
                path[i][nxt] = p | {npath}
                q.appendleft((nxt, path[i][nxt]))
    M = int(input())
    dp = [{tuple(): set()} for _ in range(M+1)]
    for i in range(M):
        u, v = map(int, input().split())
        dp[i+1] = dict(dp[i])
        for t in dp[i]:
            dp[i+1][t + (i, )] = dp[i+1][t] | path[u-1][v-1]
    ans = 0
    for key in dp[M]:
        ans += (-1) ** len(key) * 2 ** (N - len(dp[M][key]) - 1)
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
from collections import deque


def getPath(adj, start, goal):
    q = deque()
    q.appendleft((start, 0))
    while len(q):
        cur, p = q.pop()
        if cur == goal:
            return p
        for nxt, nhop in adj[cur]:
            if 2**nhop & p:
                continue
            npath = p | 2**nhop
            q.appendleft((nxt, npath))


def bitcount(x):
    return bin(x).count("1")


def main():
    N = int(input())
    adj = [set() for _ in range(N)]
    for i in range(N-1):
        a, b = map(int, input().split())
        adj[a-1].add((b-1, i))
        adj[b-1].add((a-1, i))
    M = int(input())
    dp = [0] * (2**M)
    for i in range(M):
        u, v = map(int, input().split())
        path = getPath(adj, u-1, v-1)
        for j in range(2**i):
            dp[j + 2**i] = dp[j] | path
    ans = 0
    for i in range(2**M):
        ans += (-1) ** bitcount(i) * 2 ** (N - bitcount(dp[i]) - 1)
    print(ans)


if __name__ == "__main__":
    main()