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;

namespace Abc070d
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            List<Branch> branches = new List<Branch>();
            for (int i = 0; i < n - 1; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                branches.Add(new Branch(int.Parse(input[0]), int.Parse(input[1]), int.Parse(input[2])));
            }

            string[] query = Console.ReadLine().Split(' ');
            int qNum = int.Parse(query[0]);
            int k = int.Parse(query[1]);

            Point[] points = new Point[n + 1];
            for (int i = 0; i < n; i++)
            {
                points[i + 1] = new Point();
            }
            foreach (Branch branch in branches)
            {
                points[branch.From].Add(branch);
                points[branch.To].Add(branch);
            }

            long[] dp = new long[n + 1];
            dp[k] = 0;
            List<int> queue = new List<int>();
            queue.Add(k);
            
            while (queue.Count > 0)
            {
                int current = queue[0];
                queue.RemoveAt(0);
                Point found = points[current];
                foreach (Branch branch in found)
                {
                    int other = branch.other(current);
                    if (dp[other] != 0)
                    {
                        continue;
                    }
                    dp[other] = dp[current] + branch.Distance;
                    queue.Add(other);
                }
            }

            for (int i = 0; i < qNum; i++)
            {
                string[] q = Console.ReadLine().Split(' ');
                int x = int.Parse(q[0]);
                int y = int.Parse(q[1]);

                Console.WriteLine(dp[x] + dp[y]);
            }
        }
    }

    class Point : List<Branch>
    {
    }

    class Branch
    {
        public readonly int From;
        public readonly int To;
        public readonly int Distance;

        public Branch(int from, int to, int distance)
        {
            From = from;
            To = to;
            Distance = distance;
        }

        public int other(int current)
        {
            if (current == From)
            {
                return To;
            }

            if (current == To)
            {
                return From;
            }

            throw new Exception();
        }
    }
}