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: Time Limit Exceeded)

using System;
using System.Collections.Generic;

class Procon
{
  public Procon() {}
  static void Main(string[] agrs)
  {
    new Procon().Do();
  }

  Scanner cin;

  public void Do()
  {
    cin = new Scanner();
    int N = cin.nextInt();
    int[,] dist = new int[N-1, 3];
    for (int i=0; i<N-1; i++) {
      dist[i,0] = cin.nextInt()-1;
      dist[i,1] = cin.nextInt()-1;
      dist[i,2] = cin.nextInt();
    }
    int Q = cin.nextInt();
    int K = cin.nextInt() - 1;
    long[] d = new long[N];
    for (int i=0; i<N; i++) {
      d[i] = -1;
    }
    d[K] = 0;

    for (int i=0; i<N; i++) { 
      for (int j=0; j<N-1; j++) {
        if (d[dist[j,0]] >= 0 && d[dist[j,1]] < 0) {
          d[dist[j,1]] = d[dist[j,0]] + dist[j, 2];
        } else if (d[dist[j,1]] >= 0 && d[dist[j,0]]< 0) {
          d[dist[j,0]] = d[dist[j,1]] + dist[j, 2];
        }
      }
    }

    for (int i=0; i<Q; i++) {
      int x = cin.nextInt();
      int y = cin.nextInt();
      Console.WriteLine((long)d[x-1] + (long)d[y-1]);
    }
  }
}


class Scanner
{
  string[] s;
  int i;
  int max_i;

  public Scanner()
  {
    s = new string[0];
    max_i = 0;
    i = 0;
  }

  public string nextString()
  {
    if (i >= s.Length) 
    {
      s = Console.ReadLine().Split(' ');
      max_i = s.Length;
      i = 0;
      if (max_i == 0) 
      {
        return "";
      }
      return s[i++];
    } else 
    {
      return s[i++];
    }
  }

  public int nextInt()
  {
    return int.Parse(nextString());
  }


  public long nextLong()
  {
    return long.Parse(nextString());
  }

  public double nextDouble()
  {
    return double.Parse(nextString());
  }

  public string[] arrayString()
  {
    return Console.ReadLine().Split(' ');
  }

  public int[] arrayInt()
  {
    string[] str = Console.ReadLine().Split(' ');
    int[] array = new int[str.Length];
    for (int i=0; i<str.Length; i++) 
    {
      array[i] = int.Parse(str[i]);
    }
    return array;
  }

  public long[] arrayLong()
  {
    string[] str = Console.ReadLine().Split(' ');
    long[] array = new long[str.Length];
    for (int i=0; i<str.Length; i++) 
    {
      array[i] = long.Parse(str[i]);
    }
    return array;
  }

  public double[] arrayDouble()
  {
    string[] str = Console.ReadLine().Split(' ');
    double[] array = new double[str.Length];
    for (int i=0; i<str.Length; i++) 
    {
      array[i] = double.Parse(str[i]);
    }
    return array;
  }
}