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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class Pair
{
	public int Vertex { get; private set; }
	public long Cost { get; private set; }

	public Pair(int v, long c)
	{
		Vertex = v;
		Cost = c;
	}
}


public class D
{
	public static void Main()
	{
		string[] args;

		int N = Int32.Parse(Console.ReadLine());
		List<Pair>[] graph = new List<Pair>[N+1];
		for(int i = 1; i <= N; i++)
			graph[i] = new List<Pair>();
		
		for(int i = 0; i < N-1; i++)
		{
			args = Console.ReadLine().Split(' ');
			int a = Int32.Parse(args[0]);
			int b = Int32.Parse(args[1]);
			long c = Int64.Parse(args[2]);
			graph[a].Add(new Pair(b,c));
			graph[b].Add(new Pair(a,c));
		}

		args = Console.ReadLine().Split(' ');
		int Q = Int32.Parse(args[0]);
		int K = Int32.Parse(args[1]);

		int[] x = new int[Q];
		int[] y = new int[Q];
		for(int i = 0; i < Q; i++)
		{
			args = Console.ReadLine().Split(' ');
			x[i] = Int32.Parse(args[0]);
			y[i] = Int32.Parse(args[1]);
		}

		long[] d = new long[N+1];
		for(int i = 1; i <= N; i++)
			d[i] = Int64.MaxValue;
		Queue<int> queue = new Queue<int>(N);
		d[K] = 0;
		queue.Enqueue(K);
		while(queue.Count > 0)
		{
			int v = queue.Dequeue();
			foreach(Pair pair in graph[v])
			{
				int u = pair.Vertex;
				if(d[u] < Int64.MaxValue)
					continue;
				d[u] = d[v] + pair.Cost;
				queue.Enqueue(u);
			}
		}

		for(int i = 0; i < Q; i++)
			Console.WriteLine(d[x[i]] + d[y[i]]);
	}
}