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.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;

class Program
{
    static Node[] Path;
    static long[,] Step;
    static long[] ans;
    static void Main(string[] args)
    {
        //入力を受け取る
        var N = long.Parse(Console.ReadLine());
        
        Path = new Node[N+1];
       // Step = new long[N+1,N+1];
        for(long i = 0; i< N ;i++){
          Path[i+1] = new Node();
        }
        
        for(long i = 1; i< N ;i++){
           var ABC = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
           var A = ABC[0];
           var B = ABC[1];
           var C = ABC[2];
           Path[A].adj.Add(B,C);
           Path[B].adj.Add(A,C);
           //Step[A,B] = C;
           //Step[B,A] = C;
        }
        
        var QK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var Q = QK[0];
        var K = QK[1];
        ans = new long[N+1];
        for(long i = 0;i <= N ;i++){
          ans[i] = -1;
        }
        //幅優先探索でKからの最短経路を求める
        WFS(K);
        //XからKとYからKのそれぞれの最短経路を足し合わせたものを答えにする
        for(long i = 0; i < Q ;i++){
          var XY = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
          var X = XY[0];
          var Y = XY[1];
          Console.WriteLine(ans[X]+ans[Y]);
        }
        
    }
    static void WFS(long num)
    {
        var queue = new MyQueue();
        queue.Enque(num);
        ans[num] = 0;
        while (!(queue.isEmpty()))
        {
            var top = queue.Deque();
                foreach(KeyValuePair<long,long> item in Path[top].adj) {
                    //探索済みか
                    if (ans[item.Key] == -1)
                    {
                        ans[item.Key] = ans[top] + item.Value;
                        queue.Enque(item.Key);
                    }
                }
        }
    }
}

class MyQueue
{
    public long[] datas = new long[100000];
    public long enpoint = -1;
    public long depoint = -1;
    public void Enque(long data)
    {
        this.enpoint++;
        datas[this.enpoint] = data;
    }
    public long Deque()
    {
        this.depoint++;
        return datas[this.depoint];
    }
 
    public bool isEmpty()
    {
        return (this.depoint == this.enpoint);
    }
}

class Node{
  public Dictionary<long,long> adj;
  public Node(){
    this.adj = new Dictionary<long,long>();
  }
}