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 PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
    import sys
    input = sys.stdin.buffer.readline
    from heapq import heappop, heappush
    N = int(input())
    edge = [[] for _ in range(N)]
    for i in range(N-1):
        a, b, c = (int(i) for i in input().split())
        edge[a-1].append((c, b-1))
        edge[b-1].append((c, a-1))

    def dijkstra(G, s):
        d = [10**12]*N
        used = [True] * N  # True:未確定
        d[s] = 0
        used[s] = False
        edges = []
        for e in G[s]:
            heappush(edges, e)
        while len(edges):
            c, v = heappop(edges)
            if not used[v]:
                continue
            d[v] = c
            used[v] = False
            for nexc, nexv in G[v]:
                if used[nexv]:
                    heappush(edges, (nexc+c, nexv))
        return d

    Q, K = (int(i) for i in input().split())
    dist = dijkstra(edge, K-1)
    for q in range(Q):
        x, y = (int(i)-1 for i in input().split())
        print(dist[x] + dist[y])


if __name__ == '__main__':
    main()