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.ArrayList;
import java.util.LinkedList;
import java.util.Queue;

/**
 * author @sahil
 */
class edge{
    int v;
    long w;
    edge(int uu,long ww){
        v=uu;
        w=ww;
    }
}
public class Main {
    static ArrayList<edge> adj[];
    static int n;
    static boolean vis[];
    static long dist[];
    public static void add(int u,int v,long w){
        adj[u].add(new edge(v,w));
        adj[v].add(new edge(u,w));
    }
    public static void bfs(int k){
        Queue<Integer> q=new LinkedList<>();
        vis[k]=true;
        q.add(k);
        while(!q.isEmpty()){
            int u=q.poll();
            for(edge e:adj[u]){
                if(!vis[e.v]){
                    dist[e.v]=dist[u]+e.w;
                    vis[e.v]=true;
                    q.add(e.v);
                }
            }
        }

    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(br.readLine());
        adj=(ArrayList<edge>[])new ArrayList[n];
        vis=new boolean[n];
        dist=new long[n];
        for(int i=0;i<n;++i){
            adj[i]=new ArrayList<edge>();
            vis[i]=false;
        }
        for(int i=1;i<n;++i){
            String s[]=br.readLine().split(" ");
            int u=Integer.parseInt(s[0])-1;
            int v=Integer.parseInt(s[1])-1;
            long w=Long.parseLong(s[2]);
            add(u,v,w);
        }
        String s[]=br.readLine().split(" ");
        int q=Integer.parseInt(s[0]);
        int k=Integer.parseInt(s[1])-1;
        bfs(k);
        for(int i=0;i<q;++i){
            s=br.readLine().split(" ");
            int u=Integer.parseInt(s[0])-1;
            int v=Integer.parseInt(s[1])-1;
            System.out.println(dist[u]+dist[v]);
        }
    }
}