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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    use std::io::Read;
    let mut stdin = String::new();
    std::io::stdin().read_to_string(&mut stdin).unwrap();
    let mut iter = stdin
        .split_whitespace()
        .map(|w| w.parse::<usize>().unwrap());
    let n = iter.next().unwrap();
    let mut neighbors = vec![Vec::new(); n + 1];
    for _ in 0..n - 1 {
        let a = iter.next().unwrap();
        let b = iter.next().unwrap();
        neighbors[a].push(b);
        neighbors[b].push(a);
    }
    let mut parents = vec![0; n + 1];
    let mut depth = vec![0; n + 1];
    fn visit(
        i: usize,
        p: usize,
        d: usize,
        parents: &mut Vec<usize>,
        depth: &mut Vec<usize>,
        neighbors: &Vec<Vec<usize>>,
    ) {
        parents[i] = p;
        depth[i] = d;
        for &j in &neighbors[i] {
            if j != p {
                visit(j, i, d + 1, parents, depth, neighbors);
            }
        }
    }
    visit(1, 0, 0, &mut parents, &mut depth, &neighbors);
    let m = iter.next().unwrap();
    let paths: Vec<u64> = (0..m)
        .map(|_| {
            let mut u = iter.next().unwrap();
            let mut v = iter.next().unwrap();
            let mut path = 0;
            while depth[u] > depth[v] {
                path |= 1 << u;
                u = parents[u];
            }
            while depth[v] > depth[u] {
                path |= 1 << v;
                v = parents[v];
            }
            while u != v {
                path |= 1 << u;
                u = parents[u];
                path |= 1 << v;
                v = parents[v];
            }
            path
        })
        .collect();
    let mut res: i64 = 0;
    fn dfs(paths: &[u64], edges: u64, count: u64, res: &mut i64) {
        if paths.is_empty() {
            if count & 1 == 0 {
                *res += 1 << edges.count_ones();
            } else {
                *res -= 1 << edges.count_ones();
            }
        } else {
            dfs(&paths[1..], edges, count, res);
            dfs(&paths[1..], edges & !paths[0], count + 1, res);
        }
    }
    dfs(&paths, (1 << (n + 1)) - 4, 0, &mut res);
    println!("{}", res);
}