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: Time Limit Exceeded)

use std::cmp::{min, max};
use std::collections::{HashMap, HashSet, VecDeque};

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn rooted_tree(graph: &Vec<Vec<usize>>, root: usize) -> Vec<usize> {
    let n = graph.len();
    let mut parent = vec![0; n];
    let mut visited = HashSet::new();
    visited.insert(root);
    let mut queue = VecDeque::new();
    queue.push_back(root);
    while queue.len() > 0 {
        let w = queue.pop_front().unwrap();
        for &x in &graph[w] {
            if !visited.contains(&x) {
                queue.push_back(x);
                visited.insert(x);
                parent[x] = w;
            }
        }
    }
    parent
}

fn ancestors(tree: &Vec<usize>, u: usize) -> Vec<usize> {
    let mut w = u;
    let mut result = vec![w];
    while tree[w] != 0 {
        result.push(tree[w]);
        w = tree[w];
    }
    result.reverse();
    result
}

fn lca(tree: &Vec<usize>, u: usize, v: usize) -> usize {
    let u_ancestors = ancestors(tree, u);
    let v_ancestors = ancestors(tree, v);
    let mut i = 0;
    while i < u_ancestors.len() && i < v_ancestors.len() && u_ancestors[i] == v_ancestors[i] {
        i += 1;
    }
    u_ancestors[i - 1]
}

fn main() {
    input! {
        n: usize,
        ab: [(usize, usize); n - 1],
        m: usize,
        uv: [(usize, usize); m],
    }
    let mut graph = vec![vec![]; n + 1];
    for &(ai, bi) in &ab {
        graph[ai].push(bi);
        graph[bi].push(ai);
    }
    let tree = rooted_tree(&graph, 1);
    // println!("{:?}", tree);
    let lcas = uv.iter().map(|&(u, v)| lca(&tree, u, v)).collect::<Vec<_>>();
    // println!("{:?}", lcas);

    // let paths = uv.iter().map(|&(u, v)| path(&graph, u, v)).collect::<Vec<_>>();
    // for p in &paths {
    //     println!("{:?}", p);
    // }
    let mut result = 0;
    let p = 2usize.pow(m as u32);
    for i in 0..p {
        let mut i = i;
        let mut edge_count = HashMap::new();
        for &(ai, bi) in &ab {
            edge_count.insert((min(ai, bi), max(ai, bi)), 0);
        }
        let mut path_count = 0;
        for j in 0..m {
            if i % 2 == 1 {
                path_count += 1;
                let lca = lcas[j];
                let mut w = uv[j].0;
                while w != lca {
                    *edge_count.get_mut(&(min(w, tree[w]), max(w, tree[w]))).unwrap() += 1;
                    w = tree[w];
                }
                let mut w = uv[j].1;
                while w != lca {
                    *edge_count.get_mut(&(min(w, tree[w]), max(w, tree[w]))).unwrap() += 1;
                    w = tree[w];
                }
            }
            i /= 2;
        }
        let mut zero_count = 0;
        for &v in edge_count.values() {
            if v == 0 {
                zero_count += 1;
            }
        }
        let c = 2u64.pow(zero_count as u32);
        // println!("{} {:?}", c, union);
        if path_count % 2 == 0 {
            result += c;
        } else {
            result -= c;
        }
    }
    println!("{}", result);
}