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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC070
{
    class Program
    {
        static int n;
        static long[,] M;
        static bool[] isFinal;
        static long[] d;
        static void Main()
        {
            n = int.Parse(Console.ReadLine());
            M = new long[n, n];
            isFinal = new bool[n];
            d = Enumerable.Repeat(long.MaxValue, n).ToArray();
            for (int i = 0; i < n - 1; i++)
            {
                string[] inputs = Console.ReadLine().Split(' ');
                M[int.Parse(inputs[0]) - 1, int.Parse(inputs[1]) - 1] = long.Parse(inputs[2]);
                M[int.Parse(inputs[1]) - 1, int.Parse(inputs[0]) - 1] = long.Parse(inputs[2]);
            }
            int[] qk = Console.ReadLine().Split(' ')
                        .Select(int.Parse)
                        .ToArray();
            int q = qk[0];
            int k = qk[1] - 1;
            var x = new int[q];
            var y = new int[q];
            for (int i = 0; i < q; i++)
            {
                int[] xy = Console.ReadLine().Split(' ')
                            .Select(elem => int.Parse(elem) - 1)
                            .ToArray();
                x[i] = xy[0];
                y[i] = xy[1];
            }

            Dijkstra(k);
            for (int i = 0; i < q; i++)
            {
                Console.WriteLine(d[x[i]] + d[y[i]]);
            }
        }

        static void Dijkstra(int root)
        {
            d[root] = 0;
            int u = -1;
            while (true)
            {
                long mincost = long.MaxValue;
                for (int i = 0; i < n; i++)
                {
                    if (!isFinal[i] && d[i] < mincost)
                    {
                        mincost = d[i];
                        u = i;
                    }
                }
                if (mincost == long.MaxValue || u == -1) break;
                isFinal[u] = true;

                for (int v = 0; v < n; v++)
                {
                    if (!isFinal[v] && M[u, v] != 0)
                    {
                        if (d[u] + M[u, v] < d[v])
                        {
                            d[v] = d[u] + M[u, v];
                        }
                    }
                }
            }
        }
    }
}