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.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		Graph g = new Graph(n, false);
		for(int i = 0; i < n-1; i++){
		    int from = sc.nextInt()-1;
		    int to = sc.nextInt()-1;
		    int w = sc.nextInt();
		    g.add(from, to, w);
		}
		int q = sc.nextInt();
		int k = sc.nextInt()-1;
		long[] dist = g.bfs(k);
		for(int i = 0; i < q; i++){
		    int from = sc.nextInt()-1;
		    int to = sc.nextInt()-1;
		    System.out.println(dist[from]+dist[to]);
		}
		
		// 計算
		//String result = "";
		
		
		// 出力
		//System.out.println(result);
	}
}

class Graph {
	int n;
	boolean directed;
	ArrayList<Edge>[] adjList;
	int m;
	long[] dist;
	ArrayList<Integer>[][] path;
	long INF = 1001001001001001001L;

	public Graph (int n, boolean directed) {
		this.n = n;
		this.m = 0;
		this.directed = directed;
		this.adjList = new ArrayList[n];
		for(int i = 0; i < n; i++){
			adjList[i] = new ArrayList<Edge>();
		}
		this.dist = new long[n];
		Arrays.fill(dist, INF);
	}
	
	public void add(int from, int to) {
		add(from, to, 1);
	}
	public void add(int from, int to, int w) {
		adjList[from].add(new Edge(from, to, w));
		this.m++;
		if(!directed){
			adjList[to].add(new Edge(to, from, w));
			this.m++;
		}
	}
	
	public long[] bfs(int from) { // O(M)
		dist[from] = 0;
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		q.add(from);
		while(!q.isEmpty()){
			int now = q.poll();
			for(Edge e : adjList[now]){
				if(dist[e.to] != INF) continue;
				dist[e.to] = dist[now] + e.w;
				q.add(e.to);
			}
		}
		return dist;
	}
	
	public long[] dijkstra(int from) { // O(MlogM)
		PriorityQueue<Vertex> q = new PriorityQueue<Vertex>((x, y) -> Long.compare(x.distance, y.distance));
		q.add(new Vertex(from, 0));
		dist[from] = 0;
		while(!q.isEmpty()){
			Vertex now = q.poll();
			if(now.distance > dist[now.id]) continue; 
			for(Edge e : adjList[now.id]){
				long newDist = now.distance + e.w;
				if(dist[e.to] <= newDist) continue;
				dist[e.to] = newDist;
				q.add(new Vertex(e.to, newDist));
			}
		}
		return dist;
	}
	/*
	public long[][] wf() { // O(N^3)
		for(ArrayList<Edge> list : adjList){
			for(Edge e : list){
				dist[e.from][e.to] = e.w;
			}
		}
		for(int k = 0; k < n; k++){
			for(int i = 0; i < n; i++){
				for(int j = 0; j < n; j++){
					dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
				}
			}
		}
		return dist;
	}*/
	
	public boolean bf(int from) { // O(NM)
		boolean hasNegativeLoop = false;
		for(int i = 0; i < n; i++){
			for(int j = 0; j < n; j++){
				for(Edge e : adjList[j]){
					if(dist[e.to] <= dist[e.from] + e.w) continue;
					dist[e.to] = dist[e.from] + e.w;
					if(i == n-1) hasNegativeLoop = true;
				}
			}
		}
		return hasNegativeLoop;
	}
	
	public String toString(){
		StringBuilder sb = new StringBuilder();
		for(ArrayList<Edge> list : adjList){
			for(Edge e : list){
				sb.append(e.toString());
				sb.append("\n");
			}
		}
		return sb.toString();
	}
	
	/*
	public String distToString(){
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i++){
			for(int j = 0; j < n; j++){
				if(dist[i][j] == INF){
					sb.append("from:" + i + " to:" + j + " dist:INF" + "\n");
				}else{
					sb.append("from:" + i + " to:" + j + " dist:" + dist[i][j] + "\n");
				}
			}
		}
		return sb.toString();
	}*/
	
	class Edge {
		int from;
		int to;
		int w;
		
		Edge(int from, int to, int w){
			this.from = from;
			this.to = to;
			this.w = w;
		}
		
		public String toString(){
			return "from:" + from + " to:" + to + " w:" + w;
		}
	}
	
	class Vertex {
		int id;
		long distance;
		
		Vertex(int id, long distance){
			this.id = id;
			this.distance = distance;
		}
		
		public String toString(){
			return "id:" + id + " distance:" + distance;
		}
	}
}