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.Linq;

namespace abc070_d
{
    class Program
    {
        static long[,] cost;
        static long[] d;
        static bool[] used;
        static int V;
        const long inf = 1000000000000000000;
        static void dijkstra(int start)
        {
            for (int i = 0; i < V; i++) { d[i] = inf; used[i] = false; }
            d[start] = 0;

            while (true)
            {
                int v = -1;
                for (int u = 0; u < V; u++)
                {
                    if (!used[u] && (v == -1 || d[u] < d[v])) v = u;
                }

                if (v == -1) break;
                used[v] = true;

                for (int u = 0; u < V; u++)
                {
                    d[u] = Math.Min(d[u], d[v] + cost[v, u]);
                }
            }

        }
        static void Main(string[] args)
        {
            V = int.Parse(Console.ReadLine());
            cost = new long[V, V];
            for (int i = 0; i < V; i++)
            {
                for (int j = 0; j < V; j++) cost[i, j] = inf;
            }
            d = new long[V];
            used = new bool[V];
            for (int i = 0; i < V - 1; i++)
            {
                int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
                x[0]--; x[1]--;
                cost[x[0], x[1]] = x[2]; cost[x[1], x[0]] = x[2];
            }
            int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            dijkstra(a[1] - 1);
            for (int i = 0; i < a[0]; i++)
            {
                int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
                x[0]--; x[1]--;
                Console.WriteLine(d[x[0]] + d[x[1]]);
            }
        }
    }
}