Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10000000)
def input():
    return sys.stdin.readline()[:-1]
from math import log
from bisect import *
from collections import *
from heapq import *
mod = 10**9+7

def popcnt(n):
    c = (n & 0x5555555555555555) + ((n>>1) & 0x5555555555555555)
    c = (c & 0x3333333333333333) + ((c>>2) & 0x3333333333333333)
    c = (c & 0x0f0f0f0f0f0f0f0f) + ((c>>4) & 0x0f0f0f0f0f0f0f0f)
    c = (c & 0x00ff00ff00ff00ff) + ((c>>8) & 0x00ff00ff00ff00ff)
    c = (c & 0x0000ffff0000ffff) + ((c>>16) & 0x0000ffff0000ffff)
    c = (c & 0x00000000ffffffff) + ((c>>32) & 0x00000000ffffffff)
    return c

N = int(input())
edges = [[] for i in range(N)]
edge_id = defaultdict(lambda : -1)
for i in range(N-1):
    a, b = map(lambda x: int(x)-1, input().split())
    edges[a].append(b)
    edges[b].append(a)
    edge_id[(a, b)] = edge_id[(b, a)] = i
path = defaultdict(lambda : -1)

def set_path(r, v, path_):
    visited[v] = 1
    path[(r, v)] = path_
    for u in edges[v]:
        if visited[u] == 0:
            set_path(r, u, path_ | (1 << edge_id[(v, u)]))

for i in range(N):
    visited = [0] * N
    set_path(i, i, 0)
M = int(input())
uv = [list(map(lambda x: int(x)-1, input().split())) for i in range(M)]
ans = pow(2, N-1)
for i in range(1, 1 << M):
    all_path = 0
    for j, (u, v) in enumerate(uv):
        if i & (1 << j):
            all_path |= path[(u, v)]
    if popcnt(i) & 1:
        ans -= pow(2, N-1-popcnt(all_path))
    else:
        ans += pow(2, N-1-popcnt(all_path))
print(ans)


Fixed submission:
from collections import *

def popcnt(n):
    c = (n & 0x5555555555555555) + ((n>>1) & 0x5555555555555555)
    c = (c & 0x3333333333333333) + ((c>>2) & 0x3333333333333333)
    c = (c & 0x0f0f0f0f0f0f0f0f) + ((c>>4) & 0x0f0f0f0f0f0f0f0f)
    c = (c & 0x00ff00ff00ff00ff) + ((c>>8) & 0x00ff00ff00ff00ff)
    c = (c & 0x0000ffff0000ffff) + ((c>>16) & 0x0000ffff0000ffff)
    c = (c & 0x00000000ffffffff) + ((c>>32) & 0x00000000ffffffff)
    return c

N = int(input())
edges = [[] for i in range(N)]
edge_id = defaultdict(lambda : -1)
for i in range(N-1):
    a, b = map(lambda x: int(x)-1, input().split())
    edges[a].append(b)
    edges[b].append(a)
    edge_id[(a, b)] = edge_id[(b, a)] = i
path = defaultdict(lambda : -1)

def set_path(r, v, path_):
    visited[v] = 1
    path[(r, v)] = path_
    for u in edges[v]:
        if visited[u] == 0:
            set_path(r, u, path_ | (1 << edge_id[(v, u)]))

for i in range(N):
    visited = [0] * N
    set_path(i, i, 0)
M = int(input())
uv = [list(map(lambda x: int(x)-1, input().split())) for i in range(M)]
ans = pow(2, N-1)
for i in range(1, 1 << M):
    all_path = 0
    for j, (u, v) in enumerate(uv):
        if i & (1 << j):
            all_path |= path[(u, v)]
    if popcnt(i) & 1:
        ans -= pow(2, N-1-popcnt(all_path))
    else:
        ans += pow(2, N-1-popcnt(all_path))
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10000000)
input = sys.stdin.readline
from math import log
from collections import *

class LCA:

    def __init__(self, N, root, es):
        self.N = N
        self.root = root
        self.es = es
        self.LOG_N = LOG_N = int(log(N, 2)) + 1
        self.parent = [[-1 for _ in range(N)] for _ in range(LOG_N)]
        self.depth = [0 for _ in range(N)]
        self.dfs(root, -1, 0)
        parent = self.parent
        for k in range(LOG_N-1):
            for v in range(N):
                if parent[k][v] < 0:
                    parent[k+1][v] = -1
                else:
                    parent[k+1][v] = parent[k][parent[k][v]]
        self.parent = parent

    def dfs(self, v, p, d):
        self.parent[0][v] = p
        self.depth[v] = d
        for u in self.es[v]:
            if u != p:
                self.dfs(u, v, d+1)

    def lca(self, u, v):
        LOG_N = self.LOG_N
        depth = self.depth
        parent = self.parent
        if depth[u] > depth[v]:
            t, u = u, v
            v = t
        for k in range(LOG_N):
            if (depth[v] - depth[u]) >> k & 1:
                v = parent[k][v]
        if u == v:
            return u
        for k in range(LOG_N)[::-1]:
            if parent[k][u] != parent[k][v]:
                u, v = parent[k][u], parent[k][v]
        return parent[0][u]

N = int(input())
edges = [[] for i in range(N)]
edge_id = defaultdict(lambda : -1)
for i in range(N-1):
    a, b = map(lambda x: int(x)-1, input().split())
    edges[a].append(b)
    edges[b].append(a)
    edge_id[(a, b)] = edge_id[(b, a)] = i
path_from_root = [0] * N
visited = [0] * N

def set_path(v, path):
    visited[v] = 1
    path_from_root[v] = path
    for u in edges[v]:
        if visited[u] == 0:
            set_path(u, path | (1 << edge_id[(v, u)]))

set_path(0, 0)
M = int(input())
uv = [list(map(lambda x: int(x)-1, input().split())) for i in range(M)]
tree = LCA(N, 0, edges)
popcount = lambda s: bin(s).count('1')
ans = pow(2, N-1)
for i in range(1, 1 << M):
    all_path = 0
    for j in range(M):
        if i & (1 << j):
            u, v = uv[j][0], uv[j][1]
            l = tree.lca(u, v)
            path = (path_from_root[u] | path_from_root[v]) & ~path_from_root[l]
            all_path |= path
    if popcount(i) & 1:
        ans -= pow(2, N-1-popcount(all_path))
    else:
        ans += pow(2, N-1-popcount(all_path))
print(ans)


Fixed submission:
from collections import *

def popcnt(n):
    c = (n & 0x5555555555555555) + ((n>>1) & 0x5555555555555555)
    c = (c & 0x3333333333333333) + ((c>>2) & 0x3333333333333333)
    c = (c & 0x0f0f0f0f0f0f0f0f) + ((c>>4) & 0x0f0f0f0f0f0f0f0f)
    c = (c & 0x00ff00ff00ff00ff) + ((c>>8) & 0x00ff00ff00ff00ff)
    c = (c & 0x0000ffff0000ffff) + ((c>>16) & 0x0000ffff0000ffff)
    c = (c & 0x00000000ffffffff) + ((c>>32) & 0x00000000ffffffff)
    return c

N = int(input())
edges = [[] for i in range(N)]
edge_id = defaultdict(lambda : -1)
for i in range(N-1):
    a, b = map(lambda x: int(x)-1, input().split())
    edges[a].append(b)
    edges[b].append(a)
    edge_id[(a, b)] = edge_id[(b, a)] = i
path = defaultdict(lambda : -1)

def set_path(r, v, path_):
    visited[v] = 1
    path[(r, v)] = path_
    for u in edges[v]:
        if visited[u] == 0:
            set_path(r, u, path_ | (1 << edge_id[(v, u)]))

for i in range(N):
    visited = [0] * N
    set_path(i, i, 0)
M = int(input())
uv = [list(map(lambda x: int(x)-1, input().split())) for i in range(M)]
ans = pow(2, N-1)
for i in range(1, 1 << M):
    all_path = 0
    for j, (u, v) in enumerate(uv):
        if i & (1 << j):
            all_path |= path[(u, v)]
    if popcnt(i) & 1:
        ans -= pow(2, N-1-popcnt(all_path))
    else:
        ans += pow(2, N-1-popcnt(all_path))
print(ans)