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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defmacro insert (a n val)
  (let ((arr (gensym))
        (nn (gensym)))
    `(let ((,arr ,a)
           (,nn ,n))
       (setf (aref ,arr ,nn) (cons ,val (aref ,arr ,nn))))))

(defun dfs (graph k n)
  (let ((dist (make-array n :element-type 'fixnum
                          :initial-element -1)))
    (labels
      ((proc (pos d)
         (unless (= (aref dist pos) -1) (return-from proc))
         (setf (aref dist pos) d)
         (loop for to in (aref graph pos)
               do (proc (car to) (+ d (cdr to))))))
      (proc k 0))
    dist))

(let* ((n (read))
      (graph (make-array n :element-type 'list :initial-element nil))
      (q 0) (k 0)
      (dist (make-array n :element-type 'fixnum)))
  (loop for i below (1- n)
        for a = (1- (read)) for b = (1- (read)) for c = (read)
        do (progn (insert graph a (cons b c))
                  (insert graph b (cons a c))))
  (setq q (read))
  (setq k (1- (read)))
  (setq dist (dfs graph k n))
  (loop for i below q
        for x = (1- (read)) for y = (1- (read))
        do (format t "~A~%" (+ (aref dist x) (aref dist y)))))