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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;

public class Main {

    public static class action {
        int from, to;

        action(int a, int b) {
            this.from = a;
            this.to = b;
        }
    }

    public static class edge {
        int to;
        long cost;

        edge(int b, long c) {
            this.to = b;
            this.cost = c;
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//        String[] str = br.readLine().split(" ");

        int n = Integer.parseInt(br.readLine());
        ArrayList[] edges = new ArrayList[n];
        for (int i = 0; i < n; i++) edges[i] = new ArrayList();

        for (int i = 0; i < n - 1; i++) {
            String[] str = br.readLine().split(" ");
            int a = Integer.parseInt(str[0]) - 1;
            int b = Integer.parseInt(str[1]) - 1;
            long c = Long.parseLong(str[2]);

            edge ed = new edge(b, c);
            edges[a].add(ed);
            ed = new edge(a, c);
            edges[b].add(ed);
        }

        String[] str = br.readLine().split(" ");
        int q = Integer.parseInt(str[0]);
        int k = Integer.parseInt(str[1]) - 1;
        long[] dist = new long[n];
        boolean[] reached = new boolean[n];
        Arrays.fill(reached, false);
        dist[k] = 0;
        reached[k] = true;

        ArrayDeque<Integer> que = new ArrayDeque();
        que.add(k);
        while(!que.isEmpty()){
            int node = que.poll();
            for(Object t: edges[node]){
                edge e = (edge) t;
                if(reached[e.to]) continue;

                dist[e.to] = dist[node] + e.cost;
                que.add(e.to);
                reached[e.to] = true;
            }

        }


        for (int i = 0; i < q; i++) {
            str = br.readLine().split(" ");
            int x = Integer.parseInt(str[0]) - 1;
            int y = Integer.parseInt(str[1]) - 1;
            System.out.println(dist[x] + dist[y]);
        }
    }
}