Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i.

Consider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the following M restrictions?

The i-th (1 \leq i \leq M) restriction is represented by two integers u_i and v_i, which mean that the path connecting Vertex u_i and Vertex v_i must contain at least one edge painted black.

Constraints

2 \leq N \leq 50

1 \leq a_i,b_i \leq N

The graph given in input is a tree.

1 \leq M \leq \min(20,\frac{N(N-1)}{2})

1 \leq u_i < v_i \leq N

If i \not= j, either u_i \not=u_j or v_i\not=v_j

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}
M
u_1 v_1
:
u_M v_M

Output

Print the number of ways to paint the edges that satisfy all of the M conditions.

Sample Input 1

3
1 2
2 3
1
1 3

Sample Output 1

3

The tree in this input is shown below:

All of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.

Sample Input 2

2
1 2
1
1 2

Sample Output 2

1

The tree in this input is shown below:

All of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.

Sample Input 3

5
1 2
3 2
3 4
5 3
3
1 3
2 4
2 5

Sample Output 3

9

The tree in this input is shown below:

Sample Input 4

8
1 2
2 3
4 3
2 5
6 3
6 7
8 6
5
2 7
3 5
1 6
2 8
7 8

Sample Output 4

62

The tree in this input is shown below:

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

import collections
import itertools
import sys

import numpy as np
import scipy.sparse

input = sys.stdin.readline

ri = lambda: int(input())
rs = lambda: input().rstrip()
ril = lambda: list(map(int, input().split()))
rsl = lambda: input().rstrip().split()
ris = lambda n: [ri() for _ in range(n)]
rss = lambda n: [rs() for _ in range(n)]
rils = lambda n: [ril() for _ in range(n)]
rsls = lambda n: [rsl() for _ in range(n)]

n = ri()
ls0 = [(a - 1, b - 1) for a, b in rils(n - 1)]
m = ri()
ls1 = [(u - 1, v - 1) for u, v in rils(m)]

edges = np.zeros((n, n))
for a, b in ls0:
    edges[a, b] = 1
    edges[b, a] = 1
graph = scipy.sparse.csgraph.csgraph_from_dense(edges)
_, prevs_all = scipy.sparse.csgraph.floyd_warshall(graph,
                                                   return_predecessors=True)

paths = collections.defaultdict(set)
for i, (u, v) in enumerate(ls1):
    prevs = prevs_all[u]
    x = v
    while x != u:
        y = prevs[x]
        paths[i].add(tuple(sorted([x, y])))
        x = y

res = 2**(n - 1)
for k in range(1, m + 1):
    for comb in itertools.combinations(range(m), k):
        s = set()
        for j in comb:
            s |= paths[j]
        res += (-1)**len(comb) * 2**(n - 1 - len(s))
print(res)