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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {
var inputArray = retreiveLongArray();
			var inputCount = 1;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long N = inputArray[0];

			var chotenCount = new Dictionary<long, long>();

			//頂点　<つながっている点、きょり>
			_mapinfo = new Dictionary<long, List<Tuple<long, long>>>();

			for (int i = 0; i < N-1; i++) {
				var inp= retreiveLongArray();
				var a = inp[0];
				var b = inp[1];
				var kyori = inp[2];

				if (!chotenCount.ContainsKey(a)) {
					chotenCount.Add(a, 1);
					_mapinfo.Add(a, new List<Tuple<long, long>>());
				}
				else {
					chotenCount[a]++;
				}

				if (!chotenCount.ContainsKey(b)) {
					chotenCount.Add(b, 1);
					_mapinfo.Add(b, new List<Tuple<long, long>>());
				}
				else {
					chotenCount[b]++;
				}
				//マップ作製
				_mapinfo[a].Add(new Tuple<long, long>(b, kyori));
				_mapinfo[b].Add(new Tuple<long, long>(a, kyori));

			}

			var qk = retreiveLongArray();
			var Q = qk[0];
			var K = qk[1];

			_kyoriFromK = new Dictionary<long, long>();

			//すべての頂点に対し、Kから距離を調べる
			dFS(K, 0,-1);

			var answers = new List<long>();
			for (int i = 0; i < Q; i++) {
				var inp = retreiveLongArray();
				var a = inp[0];
				var b = inp[1];

				var answer = _kyoriFromK[a] + _kyoriFromK[b];
				answers.Add(answer);
			}
			foreach (var item in answers) {
				Console.WriteLine(item);
			}

		}

		//フィールドの定義
		private static Dictionary<long, List<Tuple<long, long>>> _mapinfo;
		private static Dictionary<long, long> _kyoriFromK;



		private static void dFS(long current, long kyori, long fromChouten) {
			_kyoriFromK.Add(current, kyori);

			var hens = _mapinfo[current];

			foreach (var hen in hens) {
				if (hen.Item1 != fromChouten) {
					dFS(hen.Item1, kyori + hen.Item2, current);
				}
			}

		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}