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;
class Program
{
static long mainVertex;
static long n = long.Parse(Console.ReadLine());
static long[] howlong = new long[n];//頂点kからの距離
static List<long>[] nextList = new List<long>[n];//隣接リスト（リストの入った配列）

	static void Main()
	{
    for(int i = 0; i < n; i++) howlong[i] = -1;
    for(int i = 0; i < n; i++) nextList[i] = new List<long>();
    for(int i = 0; i < n-1; i++)
    {
    long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);//１行ごとに受け取る
    nextList[nums[0]-1].Add(nums[1]-1);//隣接リストへ追加。第2成分は距離。
    nextList[nums[0]-1].Add(nums[2]);
    nextList[nums[1]-1].Add(nums[0]-1);
    nextList[nums[1]-1].Add(nums[2]);
    }

    string[] inputSub = Console.ReadLine().Split(' ');
	  long q = long.Parse(inputSub[0]);
	  long k = long.Parse(inputSub[1]);
    k--;
    mainVertex = k;
    howlong[k] = 0;
    Length(k,0);//頂点kの、頂点kからの距離は０
    for(int i = 0; i < q; i++)
    {
    string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
    long xx = long.Parse(input[0]);
    long yy = long.Parse(input[1]);
    Console.WriteLine(howlong[xx-1]+howlong[yy-1]);
    }
	
	}

  static void Length(long vertexNum, long length)//頂点番号と、頂点kからの距離
  {
    for(int i = 0; i < nextList[vertexNum].Count(); i+=2)
    {
      long x = howlong[nextList[vertexNum][i]];
      long y = nextList[vertexNum][i+1];
      if(x == -1)
      {
        howlong[nextList[vertexNum][i]] = y + length;
        Length(nextList[vertexNum][i],howlong[nextList[vertexNum][i]]);
      }
    }
  }
  
}