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

namespace AtCoder {
    public class Program {
        static int[] getKeys() {
            var Keys = Console.ReadLine().Split(' ');
            int N = Keys.Length;
            int[] Ns = new int[N];
            for (int i = 0; i < N; i++) {
                Ns[i] = int.Parse(Keys[i]);
            }
            return Ns;
        }
        static int[] getKeys(char delimiter) {
            var Keys = Console.ReadLine().Split(delimiter);
            int N = Keys.Length;
            int[] Ns = new int[N];
            for (int i = 0; i < N; i++) {
                Ns[i] = int.Parse(Keys[i]);
            }
            return Ns;
        }

        public static void Show<T>(T[,] map) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        public static void Show<T>(T[,] map, string delimiter) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + delimiter);
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        public static void Show<T>(IEnumerable<T> ts) {
            foreach (var item in ts) {
                Console.Write(item + " ");
            }
            Console.WriteLine();
        }
        public static void Show<T>(IEnumerable<T> ts, string delimiter) {
            foreach (var item in ts) {
                Console.Write(item + delimiter);
            }
            Console.WriteLine();
        }

        static T[,] getUniform<T>(int row, int col, T value) {
            T[,] Ts = new T[row, col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    Ts[j, i] = value;
                }
            }
            return Ts;
        }
        static void setUniform<T>(T[,] ts, T value) {
            int N = ts.GetLength(0);
            int M = ts.GetLength(1);
            for (int i = 0; i < M; i++) {
                for (int j = 0; j < N; j++) {
                    ts[j, i] = value;
                }
            }
        }

        static int N, EntryNode;
        static void Main() {
            var Key = getKeys();
            N = Key[0];
            var Linked = new List<List<KeyValuePair<int, long>>>();
            for (int i = 0; i < N; i++) {
                Linked.Add(new List<KeyValuePair<int, long>>());
            }
            for (int i = 0; i < N - 1; i++) {
                Key = getKeys();
                Linked[Key[0] - 1].Add(new KeyValuePair<int, long>(Key[1] - 1, Key[2]));
                Linked[Key[1] - 1].Add(new KeyValuePair<int, long>(Key[0] - 1, Key[2]));
            }
            Key = getKeys();
            int Q = Key[0];
            EntryNode = Key[1] - 1;
            var distance = getDistanceFromEntry(Linked);
            for (int i = 0; i < Q; i++) {
                Key = getKeys();
                Console.WriteLine(distance[Key[0] - 1] + distance[Key[1] - 1]);
            }
        }


        static long[] getDistanceFromEntry(List<List<KeyValuePair<int, long>>> Linked) {
            long[] distance = new long[N];
            foreach (var item in Linked[EntryNode]) {
                distance[item.Key] = item.Value;
            }
            var Visited = new bool[N];
            Queue<int> nodes = new Queue<int>();
            nodes.Enqueue(EntryNode);
            while (nodes.Count > 0 && Visited.Any(t => t == false)) {
                var n = nodes.Dequeue();
                foreach (var item in Linked[n].Where(pair => !Visited[pair.Key])) {
                    distance[item.Key] = distance[n] + item.Value;
                    nodes.Enqueue(item.Key);
                    Visited[item.Key] = true;
                }
            }
            return distance;
        }
    }
}