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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
 
class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}
 
class Sol{
	public void Solve(){
		long Inf = (long) 1e18;
		long[] min = new long[N];
		for(int i=0;i<N;i++) min[i] = Inf;
		min[K] = 0;
		
		var q = new Queue<int>();
		q.Enqueue(K);
		while(q.Count>0){
			var now = q.Dequeue();
			foreach(var nxt in E[now]){
				if(min[nxt.Pos] != Inf) continue;
				min[nxt.Pos] = min[now] + nxt.Cost;
			}
		}
		
		var sb = new StringBuilder();
		foreach(var query in Query){
			int a = query[0], b = query[1];
			sb.AppendLine(String.Format("{0}",min[a] + min[b]));
		}
		Console.Write(sb.ToString());
	}
	int N;
	List<Pair>[] E;
	int Q,K;
	int[][] Query;

	public Sol(){
		N = ri();
		E = new List<Pair>[N];
		for(int i=0;i<N;i++) E[i] = new List<Pair>();
		for(int i=0;i<N-1;i++){
			var d = ria();
			E[d[0]-1].Add(new Pair(d[1]-1,d[2]));
			E[d[1]-1].Add(new Pair(d[0]-1,d[2]));
		}
		var dd = ria();
		Q = dd[0]; K = dd[1] - 1;
		Query = new int[Q][];
		for(int i=0;i<Q;i++){
			Query[i] = ria().Select(v => v-1).ToArray();
		}
	}
	class Pair{
		public int Pos;
		public long Cost;
		public Pair(int pos, long cost){
			Pos = pos; Cost = cost;
		}
	}
 
	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}