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;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;



public class CompetitiveProgramming
{

  public void Solve()
  {
    var N = Int1;
    var edges = new List<Tuple<long, int>>[N];
    for (int i = 0; i < N; ++i)
    {
      edges[i] = new List<Tuple<long, int>>();
    }
    for (int i = 0; i < N - 1; ++i)
    {
      var oo = Longs;
      --oo[0];
      --oo[1];
      edges[oo[0]].Add(new Tuple<long, int>(oo[2], (int)oo[1]));
      edges[oo[1]].Add(new Tuple<long, int>(oo[2], (int)oo[0]));
    }
    var ooo = Ints;
    var dist = Graph.dijkstra(edges, ooo[1] - 1);
    for (int i = 0; i < ooo[0]; ++i)
    {
      var oooo = Ints;
      Write(dist[oooo[0] - 1] + dist[oooo[1] - 1]);
    }

  }


}



public static class Graph
{
  public static long[] dijkstra(List<Tuple<long, int>>[] edge, int from, long INF = Math2.INFL)
  {
    long[] ret = Enumerable.Range(0, edge.Length).Select(_ => INF).ToArray();
    var pq = new PriorityQueue<Tuple<long, int>>((a, b) => (int)(a.Item1 - b.Item1));
    ret[from] = 0;
    pq.Enqueue(new Tuple<long, int>(0, from));
    while (pq.Count > 0)
    {
      var p = pq.Dequeue();
      var v = p.Item2;
      if (ret[v] < p.Item1) continue;
      foreach (var e in edge[v])
      {
        if (ret[e.Item2] > ret[v] + e.Item1)
        {
          ret[e.Item2] = ret[v] + e.Item1;
          pq.Enqueue(new Tuple<long, int>(ret[e.Item2], e.Item2));
        }

      }
    }
    return ret;
  }
}


public class PriorityQueue<T>
{
  List<T> _item;
  public int Count { get { return _item.Count; } }
  bool _isascend { get; set; }
  public T Peek { get { return _item[0]; } }
  Comparison<T> Comp;
  public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
  public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null)
  {
    _item = new List<T>();
    _isascend = IsAscend;
    this.Comp = cmp;
    if (list != null)
    {
      _item.AddRange(list);
      Build();
    }
  }

  private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
  private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
  private int Parent(int i)
      => (i - 1) >> 1;
  private int Left(int i)
      => (i << 1) + 1;
  public T Enqueue(T val)
  {
    int i = _item.Count;
    _item.Add(val);
    while (i > 0)
    {
      int p = Parent(i);
      if (Compare(i, p) > 0)
        Swap(i, p);
      i = p;
    }
    return val;
  }
  private void Heapify(int index)
  {
    for (int i = index, j; (j = Left(i)) < _item.Count; i = j)
    {
      if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
      if (Compare(i, j) < 0)
        Swap(i, j);
    }
  }
  public T Dequeue()
  {
    T val = _item[0];
    _item[0] = _item[_item.Count - 1];
    _item.RemoveAt(_item.Count - 1);
    Heapify(0);
    return val;
  }
  private void Build()
  {
    for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
      Heapify(i);
  }
}



public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b)
  {
    while (b > 0)
    {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007)
  {
    long ret = 1;
    long x = 1;
    for (long i = n; i >= n - r + 1; --i)
    {
      ret = ret / x * i;
      ret %= MOD;
      x++;
    }
    return ret;
  }
  public static long Comb2(long n, long r)
  {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
}
public static class Utils
{

  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N)
  {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Write(string a) => Console.WriteLine(a);
  public static void Write(params object[] i) => Write(string.Join(" ", i));
  //public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
  public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
  public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}