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)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[macro_export]
macro_rules ! chmax { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: max ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! chmin { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: min ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: max ( $ x , max ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! min { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: min ( $ x , min ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; }
#[doc = " main"]
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
    input!{
        n:usize,
        ab:[(usize,usize);n-1],
        m:usize,
        uv:[(usize,usize);m]
    }
    let mut hld = HLDecomposition::new(n);
    for (a,b) in ab {
        let a = a-1;
        let b = b-1;
        hld.connect(a, b);
    }
    hld.build(n-1);
    let path_to = |u: usize, to: usize| {
        let mut r = vec![];
        let mut u = u;
        while u != to {
            r.push(u);
            if let Some(p) = hld.par[u] {
                u = p;
            }
        }
        r
    };
    let mut cond = vec![];
    for (u,v) in uv {
        let mut x = 0;
        let u = u-1;
        let v = v-1;
        let k = hld.lca(u,v);
        for i in path_to(u,k) {
            x |= 1<<i;
        }
        for i in path_to(v,k) {
            x |= 1<<i;
        }
        cond.push(x);
    }

    let mut tot = 0;
    for mask in 1..(1<<m) {
        let mut ncond = usize::count_ones(mask) as usize;
        let mul = if ncond % 2 == 0 {
            -1
        } else {
            1
        };
        // すべての条件が
        // 使ってる枝集合
        let mut S = 0;
        for i in 0..m {
            if mask & (1<<i) > 0 {
                S |= cond[i];
            }
        }
 
        // cnt分は白で確定させないといけない。
        // 他は自由
        let cnt = usize::count_ones(S) as usize;
        tot += mul * pow2(n-1-cnt);
    }
    println!("{}", pow2(n-1) - tot);
}
fn pow2(n: usize) -> i64 {
    let mut r = 1;
    for _ in 0..n {
        r *= 2
    }
    r
}
struct HLDecomposition {
    n: usize,
    g: Vec<Vec<usize>>,
    subcnt: Vec<usize>,
    depth: Vec<usize>,
    pub par: Vec<Option<usize>>,
    heavy_next: Vec<Option<usize>>,
    heavy_head: Vec<usize>,
    real_to_virt: Vec<usize>,
    pub virt_to_real: Vec<usize>,
}
impl HLDecomposition {
    pub fn new(n: usize) -> Self {
        HLDecomposition {
            n: n,
            g: vec![vec![]; n],
            subcnt: vec![0; n],
            depth: vec![0; n],
            par: vec![None; n],
            heavy_next: vec![None; n],
            heavy_head: vec![n; n],
            real_to_virt: vec![n; n],
            virt_to_real: vec![n; n],
        }
    }
    pub fn connect(&mut self, u: usize, v: usize) {
        self.g[u].push(v);
        self.g[v].push(u);
    }
    #[doc = "O(N)"]
    pub fn build(&mut self, root: usize) {
        self.dfs1(root);
        self.dfs2(root);
        self.bfs(root);
    }
    fn dfs1(&mut self, root: usize) {
        self.depth[root] = 0;
        self.par[root] = None;
        self.dfs1_sub(root, None);
    }
    fn dfs1_sub(&mut self, u: usize, par: Option<usize>) -> usize {
        let mut cnt = 1;
        for v in self.g[u].clone() {
            if Some(v) == par {
                continue;
            }
            self.depth[v] = self.depth[u] + 1;
            self.par[v] = Some(u);
            cnt += self.dfs1_sub(v, Some(u));
        }
        self.subcnt[u] = cnt;
        cnt
    }
    fn dfs2(&mut self, root: usize) {
        self.dfs2_sub(root, None);
    }
    fn dfs2_sub(&mut self, u: usize, par: Option<usize>) {
        let mut maxv = 0;
        let mut heavy_next = None;
        let cld = self.g[u].clone();
        for &v in &cld {
            if Some(v) == par {
                continue;
            }
            if self.subcnt[v] > maxv {
                maxv = self.subcnt[v];
                heavy_next = Some(v);
            }
        }
        if let Some(hn) = heavy_next {
            self.heavy_next[u] = Some(hn);
            self.dfs2_sub(hn, Some(u));
        }
        for &v in &cld {
            if Some(v) == par || Some(v) == heavy_next {
                continue;
            }
            self.dfs2_sub(v, Some(u));
        }
    }
    fn bfs(&mut self, root: usize) {
        let mut cur_virt_id = 0;
        let mut q = VecDeque::new();
        q.push_back(root);
        while let Some(h) = q.pop_front() {
            let mut cur0 = Some(h);
            while cur0.is_some() {
                let cur = cur0.unwrap();
                self.real_to_virt[cur] = cur_virt_id;
                self.virt_to_real[cur_virt_id] = cur;
                cur_virt_id += 1;
                self.heavy_head[cur] = h;
                for v in self.g[cur].clone() {
                    if Some(v) == self.par[cur] || Some(v) == self.heavy_next[cur] {
                        continue;
                    }
                    q.push_back(v);
                }
                cur0 = self.heavy_next[cur];
            }
        }
    }
    #[doc = "O(log N)"]
    pub fn lca(&self, u: usize, v: usize) -> usize {
        let mut l = u;
        let mut r = v;
        loop {
            if self.real_to_virt[l] > self.real_to_virt[r] {
                std::mem::swap(&mut l, &mut r);
            }
            if self.heavy_head[l] == self.heavy_head[r] {
                return l;
            }
            r = self.par[self.heavy_head[r]].unwrap();
        }
    }
    #[doc = "returns a list of [l,r]. O(N)"]
    pub fn vertex_decomposition(&self) -> Vec<(usize, usize)> {
        let mut vhead = vec![self.n; self.n];
        for i in 0..self.n {
            vhead[i] = self.real_to_virt[self.heavy_head[i]];
        }
        let mut hs = std::collections::HashMap::new();
        for x in vhead {
            *hs.entry(x).or_insert(0) += 1;
        }
        let mut res = vec![];
        for (k, v) in hs {
            res.push((k, k + v - 1));
        }
        res
    }
    #[doc = "return a list of [l,r]. edge is represented by the child with larger virtual id. O(N)"]
    pub fn edge_decomposition(&self) -> Vec<(usize, usize)> {
        let V = self.vertex_decomposition();
        let mut res = vec![];
        for (u, v) in V {
            let u = if u == 0 { 1 } else { u };
            res.push((u, v));
        }
        res
    }
    #[doc = "O(logN)"]
    pub fn vertex_decomposition_between(&self, u: usize, v: usize) -> Vec<(usize, usize)> {
        let mut res = vec![];
        let mut l = u;
        let mut r = v;
        loop {
            if self.real_to_virt[l] > self.real_to_virt[r] {
                std::mem::swap(&mut l, &mut r);
            }
            let p = (
                std::cmp::max(self.real_to_virt[self.heavy_head[r]], self.real_to_virt[l]),
                self.real_to_virt[r],
            );
            res.push(p);
            if self.heavy_head[l] != self.heavy_head[r] {
                r = self.par[self.heavy_head[r]].unwrap();
            } else {
                break;
            }
        }
        res
    }
    #[doc = "O(logN)"]
    pub fn edge_decomposition_between(&self, u: usize, v: usize) -> Vec<(usize, usize)> {
        let mut res = vec![];
        let mut l = u;
        let mut r = v;
        loop {
            if self.real_to_virt[l] > self.real_to_virt[r] {
                std::mem::swap(&mut l, &mut r);
            }
            if self.heavy_head[l] != self.heavy_head[r] {
                let p = (self.real_to_virt[self.heavy_head[r]], self.real_to_virt[r]);
                res.push(p);
                r = self.par[self.heavy_head[r]].unwrap();
            } else {
                if l != r {
                    let p = (self.real_to_virt[l] + 1, self.real_to_virt[r]);
                    res.push(p);
                }
                break;
            }
        }
        res
    }
    pub fn distance(&self, u: usize, v: usize) -> usize {
        self.depth[u] + self.depth[v] - 2 * self.depth[self.lca(u, v)]
    }
}