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: Time Limit Exceeded)

from collections import deque
N = int(input())
graph = [[] * N for _ in range(N)]
graph_dist = [[0] * N for _ in range(N)]
C = [0] * (N - 1)
for i in range(N-1):
    a, b, c = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)
    graph_dist[a][b] = c
    graph_dist[b][a] = c

Q, K = map(int, input().split())
xy = [list(map(int, input().split())) for _ in range(Q)]

# BFSのためのデータ構造
dist = [-1 for _ in range(N)]   # 全頂点を未訪問に
que = deque()

# 初期条件(頂点 K-1 を初期ノードとする)
dist[K-1] = 0
que.append(K-1)

# BFS 開始(キューが空になるまで探索を行う)
while que:
    v = que[0]
    que.popleft()
    for new_v in graph[v]:
        if dist[new_v] != -1:   # すでに探索済みの頂点は探索しない
            continue
        # 新たな頂点 new_vについて距離情報を更新してキューに追加する
        dist[new_v] = dist[v] + graph_dist[v][new_v]
        que.append(new_v)


for i in range(Q):
    print(dist[xy[i][0] - 1] + dist[xy[i][1] - 1])