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: Time Limit Exceeded)

use std::io;
use std::io::BufRead;
use std::collections::{HashMap, HashSet};

const BIG: u64 = 0x4000_0000_0000_0000;

fn main() {
    let stdin = io::stdin();
    let mut stdin = stdin.lock();
    let mut s = String::new();
    stdin.read_line(&mut s).unwrap();
    let n: usize = s.trim().parse().unwrap();
    let mut v: HashMap<(usize, usize), u64> = HashMap::with_capacity(n);
    for _ in 0..(n-1) {
        let mut s = String::new();
        stdin.read_line(&mut s).unwrap();
        let t: Vec<u64> = s.trim()
                           .split_whitespace()
                           .map(|x| x.parse().unwrap())
                           .collect();
        v.insert((t[0] as usize, t[1] as usize), t[2]);
        v.insert((t[1] as usize, t[0] as usize), t[2]);
    }
    let (q, k) = {
        let mut s = String::new();
        stdin.read_line(&mut s).unwrap();
        let t: Vec<u64> = s.trim()
                           .split_whitespace()
                           .map(|x| x.parse().unwrap())
                           .collect();
        (t[0], t[1] as usize)
    };
    let mut notdone = HashSet::with_capacity(n);
    for i in 1..(n+1) {
        notdone.insert(i as usize);
    }
    let mut dist = vec![BIG; n + 1];
    notdone.remove(&k);
    dist[k] = 0;
    let mut lastdone = k;
    loop {
        let mut nextdone = 0;
        let mut cost = BIG;
        for &node in notdone.iter() {
            match v.get(&(lastdone, node)) {
                Some(c) => {
                    if dist[lastdone] + c < dist[node] {
                        dist[node] = dist[lastdone] + c;
                    }
                },
                None => {}
            }
            if dist[node] < cost {
                nextdone = node;
                cost = dist[node];
            }
        }
        if nextdone == 0 { break; }
        notdone.remove(&lastdone);
        lastdone = nextdone;
    }
    for _ in 0..q {
        let (x, y) = {
            let mut s = String::new();
            stdin.read_line(&mut s).unwrap();
            let t: Vec<usize> = s.trim()
                               .split_whitespace()
                               .map(|x| x.parse().unwrap())
                               .collect();
            (t[0], t[1])
        };
        println!("{}", dist[x] + dist[y]);
    }
}