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 OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let nei = Array.make n [] in
    for i = 1 to n - 1 do
        Scanf.scanf " %d %d %d" (fun a b c ->
            let a, b = a - 1, b - 1 in
            nei.(a) <- (c, b) :: nei.(a);
            nei.(b) <- (c, a) :: nei.(b);
        )
    done;
    Scanf.scanf " %d %d" (fun q k ->
        let k = k - 1 in
        let dist = Array.make n (max_int / n) in
        dist.(k) <- 0;
        let rec loop next = function
            | [] -> if next <> [] then loop [] next
            | hd :: tl ->
                    let cur = dist.(hd) in
                    let next = List.fold_left (fun next (c, v) ->
                        if dist.(v) > cur + c then (
                            dist.(v) <- cur + c;
                            v :: next
                        ) else next
                    ) next nei.(hd) in
                    loop next tl
        in
        loop [] [ k ];
        for i = 1 to q do
            Scanf.scanf " %d %d" (fun x y ->
                let x, y = x - 1, y - 1 in
                Printf.printf "%d\n" (dist.(x) + dist.(y))
            )
        done
    )
)