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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
public class Main {
  
  private static class Edge {
    int node;
    int weight;
    public Edge(int n, int w) {
      this.node = n;
      this.weight = w;
    }
  }
  public static void main(String[] args) { 
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      Map<Integer, List<Edge>> graph = new HashMap<>();
      for(int i = 1; i <= n; i++)
        graph.put(i, new ArrayList<>());

      for(int i = 0; i < n - 1; i++) {
        int v = sc.nextInt();
        int u = sc.nextInt();
        int w = sc.nextInt();
        Edge edge1 = new Edge(u, w);
        Edge edge2 = new Edge(v, w);
        graph.get(v).add(edge1);
        graph.get(u).add(edge2);
      }
      int qCnt = sc.nextInt();
      int k = sc.nextInt();
      Map<Integer, Long> distMap = new HashMap<>();
      bfs(k, graph, distMap);
      for(int i = 0; i < qCnt; i++)
        System.out.println(distMap.get(sc.nextInt()) + distMap.get(sc.nextInt()));
  }

  private static void bfs(int k, Map<Integer, List<Edge>> graph, Map<Integer, Long> distMap) {
    Queue<Integer> queue = new LinkedList<>();
    queue.add(k);
    Set<Integer> visited = new HashSet<>();
    visited.add(k);

    distMap.put(k, 0L);
    while(!queue.isEmpty()) {
      int node = queue.poll();
      long dist = distMap.get(node);
      for(Edge e : graph.get(node)) {
        if(visited.contains(e.node)) continue;
        distMap.put(e.node, e.weight + dist);
        queue.offer(e.node);
        visited.add(e.node);
      }
    }
  }
}