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 read<T: std::str::FromStr>(
    stdin_lock: &mut std::io::StdinLock,
    buf: &mut Vec<u8>,
    delimiter: u8,
) -> T {
    buf.clear();
    let l = std::io::BufRead::read_until(stdin_lock, delimiter, buf).unwrap();
    buf.truncate(l - 1); // remove delimiter
    let s = unsafe { std::str::from_utf8_unchecked(&buf) };
    s.parse().unwrap_or_else(|_| panic!("read"))
}

fn dfs(
    vv: &Vec<Vec<(usize, usize)>>,
    sv: usize,
    ev: usize,
    pv: usize,
    rv: &mut Vec<usize>,
) -> bool {
    if sv == ev {
        return true;
    }
    for &v in &vv[sv] {
        if v.0 == pv {
            continue;
        };
        if dfs(vv, v.0, ev, sv, rv) {
            rv.push(v.1);
            return true;
        }
    }
    return false;
}

fn main() {
    let stdin = std::io::stdin();
    let mut stdin_lock = stdin.lock();
    let mut buf: Vec<u8> = Vec::new();

    // input
    let n: usize = read(&mut stdin_lock, &mut buf, b'\n');
    let mut abv = vec![(0usize, 0usize); n - 1];
    for i in 0..n - 1 {
        abv[i].0 = read(&mut stdin_lock, &mut buf, b' ');
        abv[i].1 = read(&mut stdin_lock, &mut buf, b'\n');
    }
    let m: usize = read(&mut stdin_lock, &mut buf, b'\n');
    let mut uvv = vec![(0usize, 0usize); m];
    for i in 0..m {
        uvv[i].0 = read(&mut stdin_lock, &mut buf, b' ');
        uvv[i].1 = read(&mut stdin_lock, &mut buf, b'\n');
    }

    let mut vv = vec![Vec::new(); n + 1];
    for i in 0..n - 1 {
        let (a, b) = abv[i];
        vv[a].push((b, i));
        vv[b].push((a, i));
    }

    let mut mv = vec![0u64; m];
    for i in 0..m {
        let (u, v) = uvv[i];
        let mut rv = Vec::new();
        if dfs(&vv, u, v, u, &mut rv) {
            for e in rv {
                mv[i] |= 1u64 << e;
            }
        }
    }

    let mut ans = 0u64;
    for i in 0u64..(1u64 << m) {
        let mut mask = 0u64;
        for j in 0..m {
            if (i >> j) & 1 == 1 {
                mask |= mv[j];
            }
        }
        let c = 1u64 << ((n - 1) as u32 - mask.count_ones());
        if i.count_ones() % 2 == 0 {
            ans += c;
        } else {
            ans -= c;
        };
    }
    println!("{}", ans);
}