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: Runtime Error)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;
using System.Timers;

static class MainClass
{
    public static void Main(string[] args)
    {
        
        var N = Console.ReadLine().ToInt32();
        var dijk = new Dijkstra(N);
        

        for (int i = 0; i < N - 1; i++)
        {
            var abc = Console.ReadLine().SplittedStringToInt32List();
            var a = abc[0];
            var b = abc[1];
            var c = abc[2];
            dijk.AddPath(a, b, c);
        }
        
        var QK = Console.ReadLine().SplittedStringToInt32List();
        var Q = QK[0];
        var K = QK[1];
        var shortestpaths = new long[N + 1];
        shortestpaths[K] = 0;
        for (int i = 1; i <= N; i++)
        {
            if (i != K)
                shortestpaths[i] = dijk.GetMinCost(i, K);
        }
        for (int i = 0; i < Q; i++)
        {
            var str = Console.ReadLine().SplittedStringToInt32List();
            var x = str[0];
            var y = str[1];
            Console.WriteLine(shortestpaths[x] + shortestpaths[y]);
        }

        Console.ReadLine();
    }


    public class Dijkstra
    {
        private int maxIndex = -1;
        private const long INF = Int64.MaxValue;

        private long[,] _edgeArray;

        public Dijkstra(int size)
        {
            maxIndex = size + 1;
            _edgeArray = new long[maxIndex, maxIndex];

            for (int i = 0; i < _edgeArray.GetLength(0); i++)
            {
                for (int j = 0; j < _edgeArray.GetLength(1); j++)
                {
                    _edgeArray[i, j] = INF;
                    if (i == j) _edgeArray[i, j] = 0;
                }
            }
        }

        public void AddPath(int s, int t, int cost)
        {
            _edgeArray[s, t] = Math.Min(_edgeArray[s, t], cost);
            _edgeArray[t, s] = _edgeArray[s, t];
        }

        public long GetMinCost(int s, int t)
        {
            var cost = new long[maxIndex];
            for (int i = 0; i < cost.Length; i++) cost[i] = INF;
            cost[s] = 0;

            var priorityQueue = new PriorityQueue<ComparablePair<long, int>>(maxIndex);
            priorityQueue.Push(new ComparablePair<long, int>(0, s));

            while (priorityQueue.Count > 0)
            {
                var costDestinationPair = priorityQueue.Pop();
                if (cost[costDestinationPair.Item2] < costDestinationPair.Item1) continue;

                for (int i = 0; i < maxIndex; i++)
                {
                    long newCostToi = _edgeArray[costDestinationPair.Item2, i] == INF ? INF :
                        costDestinationPair.Item1 + _edgeArray[costDestinationPair.Item2, i];
                    if (newCostToi < cost[i])
                    {
                        cost[i] = newCostToi;
                        priorityQueue.Push(new ComparablePair<long, int>(newCostToi, i));
                    }
                }
            }

            return cost[t];
        }
    }

    public class ComparablePair<T, U> : IComparable,IComparable<ComparablePair<T,U>> where T : IComparable<T>
    {
        public readonly T Item1;
        public readonly U Item2;

        public int CompareTo(object obj)
        {
            ComparablePair<T, U> castedObj = (ComparablePair<T, U>)obj;
            return this.Item1.CompareTo(castedObj.Item1);
        }

        public int CompareTo(ComparablePair<T, U> other)
        {
            return Item1.CompareTo(other.Item1);
        }

        public ComparablePair(T t, U u)
        {
            Item1 = t;
            Item2 = u;
        }
    }


    class PriorityQueue<T>
where T : IComparable<T>
    {
        List<T> buffer;

        public PriorityQueue() { buffer = new List<T>(); }
        public PriorityQueue(int capacity) { buffer = new List<T>(capacity); }

        static void PushHeap(List<T> array, T elem)
        {
            int n = array.Count;
            array.Add(elem);

            while (n != 0)
            {
                int i = (n - 1) / 2;
                if (array[n].CompareTo(array[i]) > 0)
                {
                    T tmp = array[n]; array[n] = array[i]; array[i] = tmp;
                }
                n = i;
            }
        }


        static void PopHeap(List<T> array)
        {
            int n = array.Count - 1;
            array[0] = array[n];
            array.RemoveAt(array.Count - 1);

            for (int i = 0, j; (j = 2 * i + 1) < n;)
            {
                if ((j != n - 1) && (array[j].CompareTo(array[j + 1]) < 0))
                    j++;
                if (array[i].CompareTo(array[j]) < 0)
                {
                    T tmp = array[j]; array[j] = array[i]; array[i] = tmp;
                }
                i = j;
            }
        }


        public void Push(T elem)
        {
            PushHeap(this.buffer, elem);
        }


        public T Pop()
        {
            var data = buffer[0];
            PopHeap(buffer);
            return data;
        }

        public int Count
        {
            get { return buffer.Count; }
        }
    }
    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();

    public const int INF = int.MaxValue / 2;
    #endregion
}