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: Wrong Answer)

// This code is generated by cargo-atcoder

// Original source code:
/*
#[macro_use]
extern crate competitive;

fn main() {
    input! {
        n: usize,
        ab: [(usize1, usize1); n-1],
        m: usize,
        uv: [(usize1, usize1); m],
    }

    let mut g = vec![vec![]; n];
    for &(a, b) in ab.iter() {
        g[a].push(b);
        g[b].push(a);
    }

    let mut paths = vec![0; m];
    for (i, &(u, v)) in uv.iter().enumerate() {
        let mut path = vec![u];
        let ok = find_path(u, None, v, &g, &mut path);
        assert!(ok);

        let mut ps = 0_u32;
        for i in 0..path.len() - 1 {
            let u = path[i];
            let v = path[i + 1];

            for j in 0..ab.len() {
                if ab[j] == (u, v) || ab[j] == (v, u) {
                    ps |= 1 << j;
                    break;
                }
            }
        }
        paths[i] = ps;
    }

    let mut ans = 0;

    for b in 1_u64..(1 << m) {
        let mut ss = 0;

        for i in 0..m {
            if b & (1 << i) != 0 {
                ss |= &paths[i];
            }
        }

        let white = ss.count_ones() as usize;
        let free = (n - 1) - white;
        let num = 1 << free;

        let sign = if b.count_ones() % 2 == 0 { -1 } else { 1 };

        ans += sign * num;
    }

    println!("{}", (1 << (n - 1)) - ans);
}

fn find_path(
    u: usize,
    prev: Option<usize>,
    goal: usize,
    g: &Vec<Vec<usize>>,
    route: &mut Vec<usize>,
) -> bool {
    if u == goal {
        return true;
    }

    for &v in g[u].iter() {
        if Some(v) == prev {
            continue;
        }
        route.push(v);
        if find_path(v, Some(u), goal, g, route) {
            return true;
        }
        route.pop();
    }
    false
}

*/

fn main() {
    let exe = "./binXXXXXX";
    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().enumerate() {
        if c == b'=' { break; }
        let c = tbl[c as usize];
        if c == 64 { continue; }
        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>";