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)

using System;
using System.Collections.Generic;

namespace ABC070_D___Transit_Tree_Path
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var distance = new long[N + 1, N + 1];
            for (int i = 0; i < N - 1; i++)
            {
                var read1 = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                distance[read1[0], read1[1]] = read1[2];
                distance[read1[1], read1[0]] = read1[2];
            }

            var read2 = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var Q = read2[0];
            var K = read2[1];
            var fromK = new long[N + 1];
            for (int i = 0; i < N + 1; i++) fromK[i] = -1;
            fromK[K] = 0;
            var nodes = new Queue<int>();
            nodes.Enqueue(K);

            while (nodes.Count != 0)
            {
                var searchNode = nodes.Dequeue();
                for (int i = 1; i < N + 1; i++)
                {
                    if (distance[searchNode, i] != 0 && fromK[i] == -1)
                    {
                        nodes.Enqueue(i);
                        fromK[i] = fromK[searchNode] + distance[searchNode, i];
                    }
                }
            }

            for (int i = 0; i < Q; i++)
            {
                var xy = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                Console.WriteLine(fromK[xy[0]] + fromK[xy[1]]);
            }
        }
    }
}