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::error::Error;
use std::io;
use std::collections::{HashMap, HashSet};
use std::collections::hash_map::Entry;

fn main() {
    if let Err(e) = run() {
        println!("{}", e);
    }
}

fn run() -> Result<(), Box<Error>> {
    let mut n = String::new();
    io::stdin().read_line(&mut n)?;
    let n: usize = n.trim().parse()?;
    let mut adjs: HashMap<usize, Vec<(usize, usize)>> = HashMap::new();
    for _ in 0..n-1 {
        let mut abc = String::new();
        io::stdin().read_line(&mut abc)?;
        let abc: Vec<usize> = abc.trim().split(" ").map(|x| x.parse().expect("")).collect();
        match adjs.entry(abc[0]) {
            Entry::Occupied(o) => {o.into_mut().push((abc[1], abc[2]));},
            Entry::Vacant(v) => {v.insert(vec![(abc[1], abc[2])]);},
        };
        match adjs.entry(abc[1]) {
            Entry::Occupied(o) => {o.into_mut().push((abc[0], abc[2]));},
            Entry::Vacant(v) => {v.insert(vec![(abc[0], abc[2])]);},
        };
    }
    let mut qk = String::new();
    io::stdin().read_line(&mut qk)?;
    let qk: Vec<usize> = qk.trim().split(" ").map(|x| x.parse().expect("")).collect();
    let q = qk[0];
    let k = qk[1];
    let mut m: HashMap<usize, usize> = HashMap::new();
    let mut set: HashSet<usize> = HashSet::new();
    let mut v = Vec::new();
    for t in adjs.get(&k).unwrap() {
        v.push((t.0, t.1));
        set.insert(t.0);
    }
    while v.len() > 0 {
        let t = v.pop().unwrap();
        m.insert(t.0, t.1);
        for t2 in adjs.get(&t.0).unwrap() {
            if set.contains(&t2.0) {
                continue;
            }
            v.push((t2.0, t2.1 + t.1));
            set.insert(t2.0);
        }
    }
    for _ in 0..q {
        let mut xy = String::new();
        io::stdin().read_line(&mut xy)?;
        let xy: Vec<usize> = xy.trim().split(" ").map(|x| x.parse().expect(" ")).collect();
        let x = xy[0];
        let y = xy[1];
        println!("{}", m.get(&x).unwrap() + m.get(&y).unwrap());
    }
    Ok(())
}