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: Wrong Answer)

import java.util.*;

public class Main {
	static ArrayList<HashMap<Integer, Long>> list = new ArrayList<HashMap<Integer, Long>>();
	static long maze_cnt[];
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int a[] = new int[N];
		int b[] = new int[N];
		long c[] = new long[N];
		
		for(int i = 0; i < N; i++) {
			HashMap<Integer, Long> map = new HashMap<Integer, Long>();
			list.add(map);
		}
		
		for(int i = 0; i < N - 1; i++) {
			a[i] = sc.nextInt() - 1;
			b[i] = sc.nextInt() - 1;
			c[i] = (long)sc.nextInt();
			list.get(a[i]).put(b[i], c[i]);
			list.get(b[i]).put(a[i], c[i]);
		}
		
		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;
		}
		
		DFS(list, K);
		
		for(int i = 0; i < Q; i++) {
			System.out.println(maze_cnt[x[i]] + maze_cnt[y[i]]);
		}
	}
	
public static void DFS(ArrayList<HashMap<Integer, Long>> list, int now) {
		
		Queue<Integer> queue = new ArrayDeque<Integer>();
		queue.add(now);
		
		maze_cnt = new long[list.size()];
		boolean flag[] = new boolean[list.size()];
		
		for(int i = 0; i < list.size(); i++) {
			maze_cnt[i] = Integer.MAX_VALUE;
			flag[i] = false;
		}
		
		maze_cnt[now] = 0;
		
		while(queue.size() != 0) {
			now = queue.poll();
			for(int key : list.get(now).keySet()) {
				if(maze_cnt[key] > maze_cnt[now] + list.get(now).get(key) && !flag[key]) {
					queue.add(key);
					maze_cnt[key] = maze_cnt[now] + list.get(now).get(key);
					flag[key] = true;
				}
			}
		}
	}
}