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