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 = [];
$restriction_edges = [];
for ($i = 0; $i < $n - 1; ++$i) {
    $restriction_edges[$i] = 0;
    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;
}

$path = [1 => []];
makePath($path, 1, $edges);

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

for ($i = 0; $i < $m; ++$i) {
    fscanf(STDIN, "%d%d", $u, $v);
    foreach (findPath($u, $v, $path) as $edge_id) {
        $restriction_edges[$edge_id] += 2 ** $i;
    }
}

$answer = 0;
for ($i = 0; $i < 2 ** $m; ++$i) {
    $count = 0;
    foreach ($restriction_edges as $edge_id => $value) {
        if ($value & $i) {
            ++$count;
        }
    }

    $will_add = true;
    for ($j = 0; $j < 2 ** $m; ++$j) {
        if ($i & 2 ** $j) {
            $will_add = !$will_add;
        }
    }

    if ($will_add) {
        $answer += 2 ** ($n - 1 - $count);
    } else {
        $answer -= 2 ** ($n - 1 - $count);
    }
}

echo $answer;

function makePath(array &$path, int $target_vertex_id, array $edges): void
{
    foreach ($edges[$target_vertex_id] as $next_vertex_id => $edge_id) {
        if (isset($path[$next_vertex_id])) {
            continue;
        }
        $path[$next_vertex_id] = array_merge($path[$target_vertex_id], [$edge_id]);
        makePath($path, $next_vertex_id, $edges);
    }
}

function findPath(int $u, int $v, array $path): array
{
    $path_u = $path[$u];
    $path_v = $path[$v];

    $path_lca = array_intersect($path_u, $path_v);

    return array_diff(array_merge($path_u, $path_v), $path_lca);
}