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.Linq;
using System.Collections.Generic;

namespace abc070_d
{
	class Program
	{
		static List<Tuple<int, long>>[] d;
		static bool[] visited;
		static long[] dist;
		static void dfs(int start, long cost)
		{
			visited[start] = true;
			dist[start] = cost;
			foreach (var tup in d[start])
			{
				if (!visited[tup.Item1])
				{
					dfs(tup.Item1, cost + tup.Item2);
				}
			}
			//visited[start] = false;
		}
		static void Main(string[] args)
		{
			int V = int.Parse(Console.ReadLine());
			d = new List<Tuple<int, long>>[V]; visited = new bool[V]; dist = new long[V];
			for (int i = 0; i < V; i++) d[i] = new List<Tuple<int, long>>();
			for (int i = 0; i < V - 1; i++)
			{
				int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
				x[0]--; x[1]--;
				d[x[0]].Add(new Tuple<int, long>(x[1], x[2]));
				d[x[1]].Add(new Tuple<int, long>(x[0], x[2]));
			}
			int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
			dfs(a[1] - 1, 0);
			for (int i = 0; i < a[0]; i++)
			{
				int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
				x[0]--; x[1]--;
				Console.WriteLine(dist[x[0]] + dist[x[1]]);
			}
		}
	}
}