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: Memory Limit Exceeded)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        solve(scanner);
    }

    static void solve(Scanner scanner) {
        int N = Integer.parseInt(scanner.nextLine());
        List<List<Edge>> edges = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            edges.add(new ArrayList<>());
        }
        for (int i = 0; i < N - 1; i++) {
            int[] e = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            edges.get(e[0] - 1).add(new Edge(e[1] - 1, e[2]));
            edges.get(e[1] - 1).add(new Edge(e[0] - 1, e[2]));
        }
        String[] qv = scanner.nextLine().split(" ");
        int Q = Integer.parseInt(qv[0]);
        int via = Integer.parseInt(qv[1]) - 1;
        dist = new long[N];
        es = edges;
        getDist(via, 0);
        for (int i = 0; i < Q; i++) {
            int[] q = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            int from = q[0] - 1;
            int to = q[1] - 1;
            System.out.println(dist[from] + dist[to]);
        }
    }

    static long[] dist;
    static List<List<Edge>> es;
    static Set<Integer> used = new HashSet<>();

    static void getDist(int s, long cost) {
        used.add(s);
        dist[s] = cost;
        for (Edge next : es.get(s)) {
            if (!used.contains(next.to)) {
                getDist(next.to, cost + (long) next.cost);
            }
        }
    }

    static class Edge {
        int to;
        int cost;

        public Edge(int to, int cost) {
            this.to = to;
            this.cost = cost;
        }
    }

}