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.ArrayList;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	static final long INF = 100000000000000l;
    static final int WHITE = 0;
    static final int GRAY = 1;
    static final int BLACK = 2;
    static long[] d;
    static int N;
	static ArrayList<Edge>[] adj;
	@SuppressWarnings("unchecked")
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		int[] a = new int[N - 1];
		int[] b = new int[N - 1];
		long[] c = new long[N - 1];
		d = new long[N];
		for(int i = 0; i < N - 1; i++) {
			a[i] = sc.nextInt() - 1;
			b[i] = sc.nextInt() - 1;
			c[i] = sc.nextLong();
		}
		int Q = sc.nextInt();
		int K = sc.nextInt() - 1;
		int[] x = new int[Q];
		int[] y = new int[Q];
		for(int i = 0; i < Q; i++) {
			x[i] = sc.nextInt() - 1;
			y[i] = sc.nextInt() - 1;
		}
		sc.close();
		adj = new ArrayList[N];
		for(int i = 0; i < N; i++) {
			adj[i] = new ArrayList<Edge>();
		}
		for(int i = 0; i < N - 1; i++) {
			adj[a[i]].add(new Edge(a[i], b[i], c[i]));
			adj[b[i]].add(new Edge(b[i], a[i], c[i]));
		}
		dijkstra(K);
		for(int i = 0; i < Q; i++) {
			long ans = d[x[i]] + d[y[i]];
			System.out.println(ans);
		}
	}
	static void dijkstra(int K){
		Queue<Node> pq = new PriorityQueue<Node>(new MyComparator());
		int[] color = new int[N];
		for(int i = 0; i < N; i++) {
			d[i] = INF;
			color[i] = WHITE;
		}
		d[K] = 0;
		pq.add(new Node(K, 0l));
		while(!pq.isEmpty()) {
			Node f = pq.poll();
			int u = f.id;
			color[u] = BLACK;
			if(d[u] < f.cost) continue;
			for(int j = 0; j < adj[u].size(); j++) {
				int v = adj[u].get(j).to;
				if(color[v] == BLACK) continue;
				d[v] = d[u] + adj[u].get(j).cost;
				pq.add(new Node(v, d[v]));
				color[v] = GRAY;
			}
		}
	}
	static class Node{
		int id;
		long cost;
		public Node(int id, long cost) {
			this.id = id;
			this.cost = cost;
		}
	}
	static class MyComparator implements Comparator<Node>{
		@Override
        public int compare(Node v1, Node v2) {
			if(v1.cost < v2.cost) {
				return -1;
			}else if(v1.cost == v2.cost) {
				return 0;
			}else {
				return 1;
			}
		}
	}
	static class Edge{
		int from, to;
		long cost;
		public Edge(int from, int to, long cost) {
			this.from = from;
			this.to = to;
			this.cost = cost;
		}
	}
}