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.

Examples

Input

5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5


Output

3
2
4


Input

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


Output

5
14
22


Input

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


Output

17000000000
import java.util.*;

public class Main {
  private static final long INF = 1_000_000_000_000_000_000L;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    List<List<Dst>> from = new ArrayList<>();
    for (int i = 0; i < N; i++) {
      from.add(new ArrayList<>());
    }
    for (int i = 0; i < N-1; i++) {
      int a = sc.nextInt();
      int b = sc.nextInt();
      a--;
      b--;
      int c = sc.nextInt();
      from.get(a).add(new Dst(b,c));
      from.get(b).add(new Dst(a,c));
    }

    int Q = sc.nextInt();
    int K = sc.nextInt();
    K--;
    
    PriorityQueue<Dst> pq = new PriorityQueue<>((a,b)->{
      if (a.cost == b.cost) {
        return 0;
      }
      return a.cost > b.cost ? 1 : -1;
    });
    long[] cost = new long[N];
    Arrays.fill(cost, INF);
    
    pq.offer(new Dst(K,0));
    while (!pq.isEmpty()) {
      Dst now = null;
      while (!pq.isEmpty()) {
        now = pq.poll();
        if (cost[now.to] > 0) {
          cost[now.to] = -now.cost;
          break;
        }
      }
      if (now == null) break;
      
      for (Dst p : from.get(now.to)) {
        long newCost = now.cost+p.cost;
        if (cost[p.to] > 0 && newCost < cost[p.to]) {
          cost[p.to] = newCost;
          pq.offer(new Dst(p.to,newCost));
        }
      }
    }
      
    StringBuilder ans = new StringBuilder();
    for (int i = 0; i < Q; i++) {
      int x = sc.nextInt();
      int y = sc.nextInt();
      x--;
      y--;
      ans.append(-(cost[x]+cost[y])).append('\n');
    }
    System.out.print(ans.toString());
  }
  private static class Dst {
    private final int to;
    private final long cost;
    Dst(int to, long cost) {
      this.to = to;
      this.cost = cost;
    }
  }
}