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 Python (3.4.3) (judge verdict: Accepted)

def d_transit_tree_path(N, E, Q, K, V):
    # 頂点数、辺とそのコスト、クエリの数、経由する頂点、出発/到達頂点

    # 隣接リストの作成
    edge = [[] for _ in range(N)]
    for a, b, c in E:
        edge[a - 1].append([b - 1, c])
        edge[b - 1].append([a - 1, c])

    # Kから各節点への距離を求める
    dist = [0 for i in range(N)]  # 頂点Kからの距離
    is_visit = [False for i in range(N)]  # ある頂点が探索済か
    is_visit[K - 1] = True  # 頂点Kは探索済とする
    queue = [K - 1]  # 幅探索用キュー

    while queue:
        u = queue.pop()
        for v, c in edge[u]:
            if not is_visit[v]:
                is_visit[v] = True
                dist[v] = dist[u] + c
                queue.append(v)

    ans = ''
    for q1, q2 in V:
        ans += '{}\n'.format(dist[q1 - 1] + dist[q2 - 1])
    ans = ans[:-1]
    return ans

N = int(input())
E = [[int(i) for i in input().split()] for j in range(N-1)]
Q,K = [int(i) for i in input().split()]
V = [[int(i) for i in input().split()] for j in range(Q)]
print(d_transit_tree_path(N, E, Q, K, V))