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 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        ArrayList<Edge>[] graph = new ArrayList[n];
        for( int i = 0; i < n; i++ ) graph[i] = new ArrayList<Edge>();
        for( int i = 0; i < n-1; i++ ) {
            int u = in.nextInt()-1;
            int v = in.nextInt()-1;
            long w = in.nextLong();
            // System.out.println(u);
            // System.out.println(v);
            graph[u].add(new Edge(v, w));
            graph[v].add(new Edge(u, w));
        }
        int q = in.nextInt();
        int s = in.nextInt()-1;
        long[] dists = dijkstra(graph, s);
        // System.out.println(Arrays.toString(dists));
        for( int i = 0; i < q; i++ ) {
            int st = in.nextInt()-1;
            int ed = in.nextInt()-1;
            System.out.println(dists[st]+dists[ed]);
        }
    }
    static long[] dijkstra(ArrayList<Edge> graph[], int s) {
        int n = graph.length;
        long dist[] = new long[n];
        Arrays.fill(dist,Long.MAX_VALUE);
        PriorityQueue<Edge> pq = new PriorityQueue<>();
        dist[s] = 0; pq.offer(new Edge(s,0L));
        while(!pq.isEmpty()) {
            Edge cur = pq.poll();
            int u = cur.u;
            long w = cur.w;
            if(dist[u]<w) continue;
            for(Edge e : graph[u]) {
                int v = e.u;
                long nw = w+e.w;
                if(nw < dist[v]) {
                    dist[v] = nw;
                    pq.offer(new Edge(v,nw));
                }
            }
        }
        return dist;
    }
    public static class Edge implements Comparable<Edge> {
        public int u;
        public long w;
        public Edge( int U, long W ) {u = U; w = W;}
        public int compareTo(Edge e) {
            if( w < e.w ) return -1;
            if( w > e.w ) return 1;
            return 0;
        }
    }
}