Problem:
Score : 400 points

Problem Statement

You are given a tree with N vertices.

Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.

The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length of c_i.

You are also given Q queries and an integer K. In the j-th query (1≤j≤Q):

find the length of the shortest path from Vertex x_j and Vertex y_j via Vertex K.

Constraints

3≤N≤10^5

1≤a_i,b_i≤N (1≤i≤N-1)

1≤c_i≤10^9 (1≤i≤N-1)

The given graph is a tree.

1≤Q≤10^5

1≤K≤N

1≤x_j,y_j≤N (1≤j≤Q)

x_j≠y_j (1≤j≤Q)

x_j≠K,y_j≠K (1≤j≤Q)

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:
x_{Q} y_{Q}

Output

Print the responses to the queries in Q lines.

In the j-th line j(1≤j≤Q), print the response to the j-th query.

Sample Input 1

5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5

Sample Output 1

3
2
4

The shortest paths for the three queries are as follows:

Query 1: Vertex 2 → Vertex 1 → Vertex 2 → Vertex 4 : Length 1+1+1=3

Query 2: Vertex 2 → Vertex 1 → Vertex 3 : Length 1+1=2

Query 3: Vertex 4 → Vertex 2 → Vertex 1 → Vertex 3 → Vertex 5 : Length 1+1+1+1=4

Sample Input 2

7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7

Sample Output 2

5
14
22

The path for each query must pass Vertex K=2.

Sample Input 3

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

Sample Output 3

17000000000

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use std::cmp;
use std::cmp::Ordering;
use std::collections::BinaryHeap;

// read a line(without line feed)
fn read_line() -> String {
    let mut in_str = String::new();
    io::stdin().read_line(&mut in_str).unwrap();
    return in_str.trim().to_string();
}

// read wods on a line
pub fn read_words_in_line() -> Vec<String> {
    let s = read_line();
    return s.split_whitespace().map(|x| x.to_string()).collect::<Vec<String>>()
}

// read type t on a line
pub fn read_t_in_line<T : std::str::FromStr>() -> Vec<T> {
    let mut v : Vec<T> = Vec::new();
    for e in read_words_in_line().iter().map(|x| x.parse::<T>()) {
        if let Ok(r) = e {
            v.push(r);
        }
        else{
            return Vec::new();
        }
    }
    return v;
}

// sort slice
pub fn sort<T : std::cmp::Ord>(slice : &mut [T]) {
    slice.sort();
}
// sort slice by reverse order
pub fn sort_rev<T : std::cmp::Ord>(slice : &mut [T]) {
    slice.sort_by(|x, y| y.cmp(x));
}

pub fn min<T : std::cmp::Ord>(a : T, b : T) -> T{
    return cmp::min(a, b);
}

pub fn max<T : std::cmp::Ord>(a : T, b : T) -> T{
    return cmp::max(a, b);
}

#[derive(Copy, Clone, Eq, PartialEq, Debug)]
struct State {
    cost     : i32,
    node     : i32,
    vismask  : i32
}

impl Ord for State {
    fn cmp(&self, other: &State) -> Ordering {
        other.cost.cmp(&self.cost)
    }
}

impl PartialOrd for State {
    fn partial_cmp(&self, other : &State) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}


fn main() {

    let n = read_t_in_line::<i64>()[0];
    let mut g = vec![vec![] ; n as usize];

    for _ in 0..n-1 {
        let l = read_t_in_line::<i64>();
        let (mut a, mut b, c) = (l[0], l[1], l[2]);
        a -= 1;
        b -= 1;
        g[a as usize].push((b, c));
        g[b as usize].push((a, c));
    }

    let l = read_t_in_line::<i64>();
    let (q, mut k) = (l[0], l[1]);
    k -= 1;
    
    let qs : Vec<_> =
        (0..q).
        map(|_| read_t_in_line::<i64>()).
        map(|l| (l[0] - 1, l[1] - 1)).collect();

    let mut dist = vec![i64::max_value() ; n as usize];
    let mut pq = BinaryHeap::new();

    pq.push((0 as i64, k));
    dist[k as usize] = 0 as i64;

    while let Some((mut ccost, cpos)) = pq.pop() {
        ccost *= -1;
        if ccost > dist[cpos as usize] {
            continue;
        }
        for &(npos, w) in &g[cpos as usize] {
            let ncost = ccost + w;
            if ncost < dist[npos as usize] {
                dist[npos as usize] = ncost;
                pq.push((-ncost, npos))
            }
        }
    }

    for (x, y) in qs {
        let ans = dist[x as usize] + dist[y as usize];
        println!("{}", ans);
    }

}