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::vec::Vec;
use std::cmp::*;
use std::collections::BinaryHeap;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
  let n: usize = read();
  let mut g: Vec<Vec<(usize, u64)>> = vec![vec![]; n];
  for _ in 0..n-1 {
    let v: Vec<usize> = read_vec();
    g[v[0] - 1].push((v[1] - 1, v[2] as u64));
    g[v[1] - 1].push((v[0] - 1, v[2] as u64));
  }

  let (q, k) = {
    let v: Vec<usize> = read_vec();
    (v[0], v[1] - 1)
  };

  let mut tasks = Vec::new();
  for _ in 0..q {
    let v: Vec<usize> = read_vec();
    tasks.push((v[0] - 1, v[1] - 1));
  }

  //dijkstra法による単一始点からの最短経路長を探索
  let dist = dijkstra(n, &g, k);

  for (x, y) in tasks {
    println!("{}", dist[x] + dist[y]);
  }
}


fn dijkstra(n: usize, adj_list: &Vec<Vec<(usize, u64)>>, start: usize) -> Vec<u64> {
  let mut dist = vec![std::u64::MAX; n];
  let mut p_queue: BinaryHeap<(i64, usize)> = BinaryHeap::new();

  //init
  dist[start] = 0;
  p_queue.push((0, start));

  while !p_queue.is_empty() {
    // 起点となるノード
    let (cost, now)
      = match p_queue.pop() {
        None => break,
        Some(e) => (-e.0 as u64, e.1),
      };

    // 繋がっているノードを探索
    for &edge in &adj_list[now] {
      let next = edge.0;
      let weight = edge.1;

      if dist[next] > weight + cost {
        p_queue.push((-((weight + cost) as i64), next));
        dist[next] = weight + cost;
      }
    }

  }

  dist
}