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)

def dijkstra(start, matrix, n):
    d = [float("inf")] * n
    fixed = [False] * n
    fixed[start] = True
    d[start] = 0
    now = start

    while True:
        rep = -1
        dist = float("inf")
        for i in range(n):
            if not fixed[i]:
                if (0 <= matrix[now][i]):
                    d[i] = d[now] + matrix[now][i]
                if d[i] < dist:
                    rep = i
                    dist = d[i]
        if rep == -1:
            break
        fixed[rep] = True
        now = rep
        for i in range(n):
            if (0 <= matrix[now][i]):
                cost = d[now] + matrix[now][i]
                if (0 <= cost < d[i]):
                    d[i] = cost
    return d


n = int(input().strip())
matrix = [[-1] * n for _ in range(n)]
for i in range(n - 1):
    a, b, c = map(int, input().split())
    a -= 1
    b -= 1
    matrix[a][b] = c
    matrix[b][a] = c
q, k = map(int, input().split())
k -= 1
queries = [tuple(map(int, input().split())) for _ in range(q)]
from_k = dijkstra(k, matrix, n)
for query in queries:
    start = query[0] - 1
    goal = query[1] - 1
    print(from_k[start] + from_k[goal])