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)

#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 edge = new List<Edge>[N];
        for (int i = 0; i < N; i++)
        {
            edge[i] = new List<Edge>();
        }
        for (int i = 0; i < N - 1; i++)
        {
            var abc = Console.ReadLine().SplittedStringToInt32List();
            var a = abc[0] - 1;
            var b = abc[1] -1 ;
            var c = abc[2];
            edge[a].Add(new Edge() { To = b, Cost = c });
            edge[b].Add(new Edge() { To = a, Cost = c });
        }
        
        var QK = Console.ReadLine().SplittedStringToInt32List();
        var Q = QK[0];
        var K = QK[1] - 1;

        var queue = new Queue<Point>();
        queue.Enqueue(new Point() { CostFromStart = 0, Number = K });
        var costs = new long[N];
        
        while (queue.Count() != 0)
        {
            var item = queue.Dequeue();
            foreach (var item2 in edge[item.Number])
            {
                if (costs[item2.To] != 0)
                    continue;
                costs[item2.To] += item2.Cost + costs[item.Number];
                var p = new Point() { Number = item2.To, CostFromStart = costs[item2.To] };
                queue.Enqueue(p);
            }
        }
        for (int i = 0; i < Q; i++)
        {
            var str = Console.ReadLine().SplittedStringToInt32List();
            var x = str[0] -1 ;
            var y = str[1] -1;
            Console.WriteLine(costs[x] + costs[y]);
        }

        Console.ReadLine();
    }

    public class Edge
    {
        public int To;
        public int Cost;
    }

    public class Point
    {
        public int Number;
        public long CostFromStart;
    }

    #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
}