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;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("5");
            WillReturn.Add("1 2 1");
            WillReturn.Add("1 3 1");
            WillReturn.Add("2 4 1");
            WillReturn.Add("3 5 1");
            WillReturn.Add("3 1");
            WillReturn.Add("2 4");
            WillReturn.Add("2 3");
            WillReturn.Add("4 5");
            //3
            //2
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("7");
            WillReturn.Add("1 2 1");
            WillReturn.Add("1 3 3");
            WillReturn.Add("1 4 5");
            WillReturn.Add("1 5 7");
            WillReturn.Add("1 6 9");
            WillReturn.Add("1 7 11");
            WillReturn.Add("3 2");
            WillReturn.Add("1 3");
            WillReturn.Add("4 5");
            WillReturn.Add("6 7");
            //5
            //14
            //22
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("10");
            WillReturn.Add("1 2 1000000000");
            WillReturn.Add("2 3 1000000000");
            WillReturn.Add("3 4 1000000000");
            WillReturn.Add("4 5 1000000000");
            WillReturn.Add("5 6 1000000000");
            WillReturn.Add("6 7 1000000000");
            WillReturn.Add("7 8 1000000000");
            WillReturn.Add("8 9 1000000000");
            WillReturn.Add("9 10 1000000000");
            WillReturn.Add("1 1");
            WillReturn.Add("9 10");
            //17000000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static int N;

    //辺の情報
    struct EdgeInfoDef
    {
        internal int ToPos;
        internal long Cost;
    }
    //隣接リストで、辺の情報のList[頂点番号]を管理
    static Dictionary<int, List<EdgeInfoDef>> mEdgeInfoDict =
        new Dictionary<int, List<EdgeInfoDef>>();

    static int K;

    //Kからの距離[頂点番号]な配列
    static long[] mKyoriArr;

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        N = int.Parse(InputList[0]);

        for (int I = 1; I <= N - 1; I++) {
            SplitAct(InputList[I]);
            int A = wkArr[0];
            int B = wkArr[1];
            int C = wkArr[2];

            if (mEdgeInfoDict.ContainsKey(A) == false)
                mEdgeInfoDict.Add(A, new List<EdgeInfoDef>());
            if (mEdgeInfoDict.ContainsKey(B) == false)
                mEdgeInfoDict.Add(B, new List<EdgeInfoDef>());

            mEdgeInfoDict[A].Add(new EdgeInfoDef() { ToPos = B, Cost = C });
            mEdgeInfoDict[B].Add(new EdgeInfoDef() { ToPos = A, Cost = C });
        }

        SplitAct(InputList[N]);
        K = wkArr[1];

        ExecDFS();

        //Console.WriteLine("K({0})から各頂点までの距離", K);
        //for (int I = 1; I <= N; I++) {
        //    Console.WriteLine("mKyoriArr[{0}]={1}", I, mKyoriArr[I]);
        //}

        //問い合わせの処理
        for (int I = N + 1; I <= InputList.Count - 1; I++) {
            SplitAct(InputList[I]);
            int X = wkArr[0];
            int Y = wkArr[1];

            long Answer = 0;
            Answer += mKyoriArr[X];
            Answer += mKyoriArr[Y];
            Console.WriteLine(Answer);
        }
    }

    struct JyoutaiDef
    {
        internal int CurrPos;
        internal long CostSum;
    }

    //深さ優先探索でKから各頂点までの距離を求める
    //距離[頂点番号]な配列を求める
    static void ExecDFS()
    {
        mKyoriArr = new long[N + 1];

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.CurrPos = K;
        WillPush.CostSum = 0;
        mKyoriArr[K] = 0;
        Stk.Push(WillPush);

        var VisitedSet = new HashSet<int>();
        VisitedSet.Add(K);

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();

            mKyoriArr[Popped.CurrPos] = Popped.CostSum;

            foreach (EdgeInfoDef EachEdgeInfo in mEdgeInfoDict[Popped.CurrPos]) {
                WillPush.CurrPos = EachEdgeInfo.ToPos;
                WillPush.CostSum = Popped.CostSum + EachEdgeInfo.Cost;

                //再訪禁止
                if (VisitedSet.Add(WillPush.CurrPos) == false)
                    continue;

                Stk.Push(WillPush);
            }
        }
    }
}