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.Generic;

class ABC070D
{
	static public void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		List<int>[] dest = new List<int>[N+1];
		for(int i=1; i<=N; i++)
		{
			dest[i] = new List<int>();
		}
		List<long>[] cost = new List<long>[N+1];
		for(int i=1; i <= N; i++)
		{
			cost[i] = new List<long>();
		}

		int a, b;
		long c;
		string[] vals;
		for(int i=1; i <= N-1; i++)
		{
			vals = Console.ReadLine().Split(' ');
			a = int.Parse(vals[0]);
			b = int.Parse(vals[1]);
			c = long.Parse(vals[2]);
			dest[a].Add(b);
			cost[a].Add(c);
			dest[b].Add(a);
			cost[b].Add(c);
		}
		int Q,K;
		vals = Console.ReadLine().Split(' ');
		Q = int.Parse(vals[0]);
		K = int.Parse(vals[1]);
		long[] distance = new long[N+1];
		distance[K] = 0;
		Queue<int> q = new Queue<int>();
		q.Enqueue(K);
		int t;
		while(q.Count > 0)
		{
			t = q.Dequeue();
			for(int i=0; i < dest[t].Count; i++)
			{
				if(distance[dest[t][i]] > 0)
					continue;
				distance[dest[t][i]] = distance[t] + cost[t][i];
				q.Enqueue(dest[t][i]);
			}
		}
		int[,] query = new int[Q, 2];
		for(int i=0; i < Q; i++)
		{
			vals = Console.ReadLine().Split(' ');
			query[i,0] = int.Parse(vals[0]);
			query[i,1] = int.Parse(vals[1]);
		}
		for(int i=0; i < Q; i++)
		{
			Console.WriteLine(distance[query[i,0]] + distance[query[i,1]]);
		}
	}
}