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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php

fscanf(STDIN, "%d", $n);

$edges = [];
for ($i = 0; $i < $n - 1; ++$i) {
    fscanf(STDIN, "%d%d", $a, $b);

    if (!isset($edges[$a])) {
        $edges[$a] = [];
    }

    if (!isset($edges[$b])) {
        $edges[$b] = [];
    }

    $edges[$a][$b] = $i;
    $edges[$b][$a] = $i;
}

fscanf(STDIN, "%d", $m);

$restriction_list = [['term_num' => 0, 'paths' => []]];
for ($i = 0; $i < $m; ++$i) {
    fscanf(STDIN, "%d%d", $u, $v);

    $new_restriction = getPath(['is_found' => false, 'edge_list' => []], $u, $v, $edges);

    $new_restrictions = [];
    foreach ($restriction_list as $restrictions) {
        ++$restrictions['term_num'];
        $restrictions['paths'] = array_unique(array_merge($restrictions['paths'], $new_restriction['edge_list']));
        $new_restrictions[] = $restrictions;
    }

    $restriction_list = array_merge($restriction_list, $new_restrictions);
}

$answer = 0;
foreach ($restriction_list as $restrictions) {
    if ($restrictions['term_num'] % 2 === 0) {
        $answer += 2 ** ($n - 1 - count($restrictions['paths']));
    } else {
        $answer -= 2 ** ($n - 1 - count($restrictions['paths']));
    }
}
echo $answer;

function getPath(array $log, int $from_id, int $to_id, array $edges): array
{
    if ($log['is_found']) {
        return $log;
    }

    foreach ($edges[$from_id] as $next_vertex_id => $edge) {
        $log['edge_list'][] = $edge;

        if ($next_vertex_id === $to_id) {
            $log['is_found'] = true;
            return $log;
        }

        unset($edges[$next_vertex_id][$from_id]);
        $res_from_next_vertex = getPath($log, $next_vertex_id, $to_id, $edges);
        if ($res_from_next_vertex['is_found']) {
            return $res_from_next_vertex;
        } else {
            $log['edge_list'] = array_filter($log['edge_list'], function ($path_edge) use ($edge) {
                return $path_edge !== $edge;
            });
        }
    }

    return $log;
}