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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn dfs(tree: &Vec<Vec<(usize, usize)>>, v: usize, tv: usize, p: usize) -> Option<Vec<usize>> {
    if v == tv {
        return Some(vec![]);
    }
    for (t, e) in &tree[v] {
        if *t == p {
            continue;
        }
        if let Some(mut res) = dfs(tree, *t, tv, v) {
            res.push(*e);
            return Some(res);
        }
    }
    None
}

fn main() {
    input! {
        n : usize,
        edge : [(Usize1,Usize1); n-1],
        m : usize,
        path : [(Usize1,Usize1); m]
    }
    let mut tree = vec![vec![]; n];
    for (i, (a, b)) in edge.iter().enumerate() {
        tree[*a].push((*b, i));
        tree[*b].push((*a, i));
    }

    let path = path
        .iter()
        .map(|(u, v)| {
            dfs(&tree, *u, *v, *u)
                .unwrap()
                .iter()
                .fold(0u64, |s, x| s | (1u64 << x))
        })
        .collect::<Vec<_>>();

    let mut res = 0;
    for i in 0u64..1 << m {
        let mut s = 0;
        for j in 0..m {
            if (i >> j) & 1 == 1 {
                s |= path[j];
            }
        }
        let x = 1u64 << (n - 1 - s.count_ones() as usize);
        if i.count_ones() % 2 == 1 {
            res -= x;
        } else {
            res += x;
        }
    }
    println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/binA4AA20E0";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";