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::{fastout, input};

#[derive(Clone)]
struct Edge {
    to: i64,
    id: i64,
}

fn collect(g: &Vec<Vec<Edge>>, u: i64, v: i64, p: i64) -> Option<i64> {
    if u == v {
        return Some(0);
    }
    for e in g[u as usize].iter() {
        if e.to == p {
            continue;
        }
        if let Some(s) = collect(g, e.to, v, u) {
            return Some(s | (1 << e.id));
        }
    }
    return None;
}

#[fastout]
fn main() {
    input! { n: i64 }
    let g = &mut vec![vec![]; n as usize];
    for i in 0..n - 1 {
        input! { a: i64, b: i64 }
        let a = a - 1;
        let b = b - 1;
        g[a as usize].push(Edge {
            to: b,
            id: i as i64,
        });
        g[b as usize].push(Edge {
            to: a,
            id: i as i64,
        });
    }
    input! { m: i64 }
    let mut paths = vec![0; m as usize];
    for j in 0..m {
        input! { u: i64, v: i64 }
        let u = u - 1;
        let v = v - 1;
        paths[j as usize] = collect(g, u, v, -1).unwrap();
    }
    let mut ans: i64 = 0;
    for s in 0..(1 << m) as i64 {
        let mut mask = 0;
        for j in 0..m {
            if (s >> j) & 1 == 1 {
                mask |= paths[j as usize];
            }
        }
        if s.count_ones() % 2 == 0 {
            ans += 1 << (n - 1 - mask.count_ones() as i64);
        } else {
            ans -= 1 << (n - 1 - mask.count_ones() as i64);
        }
    }
    println!("{}", ans);
}

*/

fn main() {
    let exe = "/tmp/bin1CAF1DE9";
    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>";