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 Java8 (OpenJDK 1.8.0) (judge verdict: Memory Limit Exceeded)

import java.util.*;

public class Main {
  static long[] dp;
  static ArrayList[] edge;
  static long[][] cost;
  //static HashMap<int[], Long> cost;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    dp = new long[n];
    edge = new ArrayList[n];
    cost = new long[n][n];
    for(int i = 0; i < n; i++) {
      edge[i] = new ArrayList<Integer>();
    }
    for(int i = 0; i < n - 1; i++) {
      int a = sc.nextInt() - 1;
      int b = sc.nextInt() - 1;
      int[] e1 = {a, b};
      int[] e2 = {b, a};
      long c = sc.nextLong();
      cost[a][b] = c;
      cost[b][a] = c;
      edge[a].add(b);
      edge[b].add(a);
    }
    int Q = sc.nextInt();
    int K = sc.nextInt() - 1;
    dfs(K, -1);
    for(int i = 0; i < Q; i++) {
      int x = sc.nextInt() - 1;
      int y = sc.nextInt() - 1;
      System.out.println(dp[x] + dp[y]);
    }
  }

  public static void dfs(int v, int parent) {
    ArrayList<Integer> e = edge[v];
    if((parent >= 0) && (e.size() == 1)) {
      
    } else {
      for(int i = 0; i < e.size(); i++) {
        int u = e.get(i);
        if(u != parent) {
          long c = cost[u][v];
          dp[u] = dp[v] + c;
          dfs(u, v);
        }
      }
    }
  }
}

class Edge {
  int u;
  int v;
  Edge(int u, int v) {
    this.u = u;
    this.v = v;
  }
}