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: Memory Limit Exceeded)

import java.util.*;

public class Main {

	class State implements Comparable<State>{
		int now;
		long cost;
		public State(int now, long cost) {
			this.now = now;
			this.cost = cost;
		}
		public int compareTo(State o) {
			if(this.cost > o.cost) return 1;
			if(this.cost < o.cost) return -1;
			return 0;
		}
	}
	
	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			int n = sc.nextInt();
			long [][] pass = new long[n][n];
			for(int i = 0; i < n;i++){
				Arrays.fill(pass[i], Long.MAX_VALUE);
			}
			
			for(int i =0; i < n-1; i++){
				int a = sc.nextInt() - 1;
				int b = sc.nextInt() - 1; 
				int c = sc.nextInt();
				pass[a][b] = c;
				pass[b][a] = c;
			}
			int q = sc.nextInt();
			int start = sc.nextInt() -1;
			
			PriorityQueue<State> open = new PriorityQueue<>();
			open.add(new State(start, 0));
			long [] close = new long[n];
			Arrays.fill(close, Long.MAX_VALUE);
			
			boolean [] used = new boolean[n];
			used[start] = true;
			int count = 1;
			
			while(!open.isEmpty()){
				State current = open.poll();
				if(!used[current.now]){
					used[current.now] = true;
					count++;
					if(count == n){
						break;
					}
				}
				
				for(int i = 0; i < n;i++){
					if(current.now == i)continue;
					if(pass[current.now][i] == Long.MAX_VALUE ) continue;
					long nextcost = current.cost + pass[current.now][i];
					if(close[i] < nextcost) continue;
					close[i] = nextcost;
					open.add(new State(i, nextcost));
				}
			}
			
			StringBuilder sb = new StringBuilder();
			for(int i = 0; i < q; i++){
				int x = sc.nextInt() - 1;
				int y = sc.nextInt() - 1;
				long res = close[x] + close[y];
				sb.append(res+"\n");
			}
			System.out.print(sb.toString());
		}

	}


	private void debug(Object... o) {
		System.out.println("debug = " + Arrays.deepToString(o));
	}

	public static void main(String[] args) {
		new Main().doit();
	}

}