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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

	public void Proc()
	{
        int nodeCount = int.Parse(Reader.ReadLine());
        this.TreeNodeList = new TreeNode[nodeCount];

        for (int i = 0; i < nodeCount - 1; i++) {
            long[] inpt = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
            int[] node = inpt.Take(2).Select(a => (int)a - 1).ToArray();
            node.ToList().ForEach(a=>{
                if(!dic.ContainsKey(a)) {
                    dic.Add(a, new Dictionary<int, long>());
                }
            });
            dic[node[0]].Add(node[1], inpt[2]);
            dic[node[1]].Add(node[0], inpt[2]);
        }

        int[] tmp = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
        this.Query = new int[tmp[0]][];
        this.MustThuruPoint = tmp[1]-1;

        for (int i = 0; i < Query.Length; i++) {
            Query[i] = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)-1).OrderBy(a => a).ToArray();
        }

        TreeNodeList[0] = new TreeNode(0);

        Queue<int> que = new Queue<int>();
        dic[0].ToList().ForEach(a =>
        {
            TreeNodeList[a.Key] = TreeNodeList[0].Add(a.Key, a.Value);
            que.Enqueue(a.Key);
        });
        while(que.Count()>0) {
            int current = que.Dequeue();
            dic[current].ToList().ForEach(a=>{
                if(a.Key != TreeNodeList[current].Parent.Id) {
                    TreeNodeList[a.Key] = TreeNodeList[current].Add(a.Key, a.Value);
                    que.Enqueue(a.Key);
                }                
            });
        }
        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < Query.Length; i++) {
            ans.AppendLine(GetAns(Query[i][0], Query[i][1]).Length.ToString());
        }
        Console.Write(ans.ToString());
    }

    private Route GetAns(int node1, int node2) {
        if(node1 == node2) {
            Route tmp = new Route();
            tmp.CommonParent = TreeNodeList[node1];
            tmp.ThuruPoint = node1 == this.MustThuruPoint;
            return tmp;
        }

        Route ans = new Route();
        if(TreeNodeList[node1].Depth > TreeNodeList[node2].Depth) {
            ans = GetAnsSub(node2, node1);
        } else {
			ans = GetAnsSub(node1, node2);
		}
        if(ans.ThuruPoint) {
            return ans;
        }
        Route ret = GetAnsSub(MustThuruPoint, ans.CommonParent.Id);
        ans.Length += ret.Length * 2;
        return ans;
    }

    private Route GetAnsSub(int node1, int node2) {
		if (node1 == node2)
		{
			Route tmp = new Route();
			tmp.CommonParent = TreeNodeList[node1];
			tmp.ThuruPoint = node1 == this.MustThuruPoint;
			return tmp;
		}

        if (!pathDic.ContainsKey(node1))
		{
			pathDic.Add(node1, new Dictionary<int, Route>());
		}
		if (pathDic[node1].ContainsKey(node2))
		{
			return pathDic[node1][node2].Duplicate();
		}
        if(TreeNodeList[node1].Depth > TreeNodeList[node2].Depth) {
            return GetAnsSub(node2, node1);
        }
        Route ans = GetAnsSub(node1, TreeNodeList[node2].Parent.Id);
        ans.Length += TreeNodeList[node2].Length;
        if(node2 == MustThuruPoint) {
            ans.ThuruPoint = true;
        }
        pathDic[node1][node2] = ans;
        return ans;
	}

    private class Route {
        public long Length;
        public bool ThuruPoint = false;
        public TreeNode CommonParent = null;
        public Route Duplicate() {
            Route tmp = new Route();
            tmp.Length = this.Length;
            tmp.ThuruPoint = this.ThuruPoint;
            tmp.CommonParent = this.CommonParent;
            return tmp;
        }
    }

    private Dictionary<int, Dictionary<int, Route>> pathDic = new Dictionary<int, Dictionary<int, Route>>();


    private int MustThuruPoint = 0;
    private int[][] Query;

    private Dictionary<int, Dictionary<int, long>> dic = new Dictionary<int, Dictionary<int, long>>();

    private TreeNode[] TreeNodeList;
    private class TreeNode {
        public int Id;
        public long Length;
        public TreeNode Parent;
        public List<TreeNode> Items = new List<TreeNode>();
        public int Depth = 0;

        public TreeNode(int id) {
            this.Id = id;
        }
        public TreeNode Add(int num, long len) {
            TreeNode item = new TreeNode(num);
            item.Parent = this;
            item.Depth = this.Depth + 1;
            this.Items.Add(item);
            item.Length = len;
            return item;
        }
    }


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"



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


";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}