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)

import sys
sys.setrecursionlimit(10**9)
n = int(input())
visited = [0]*n
dist = [0]*n
edge = [[] for _ in range(n)]
def dfs(k):
    visited[k]=1
    for i in edge[k]:
        if visited[i[0]]==0:
            dist[i[0]]=i[1]+dist[k]
            dfs(i[0])


    return dist
def main():

    for i in range(n-1):
        a,b,c=map(int, input().split())
        edge[a-1].append([b-1,c])
        edge[b-1].append([a-1,c])

    q,k=map(int, input().split())
    #頂点kから各頂点への距離を最初に求めておくdist[i]:頂点kから頂点iまでの距離　 dist[k]=0

    visited[k-1]=1
    dist = dfs(k-1)

    res = [0]*q
    for i in range(q):
        x,y=map(int, input().split())
        res[i]=dist[x-1]+dist[y-1]


    for i in range(q):
        print(res[i])
if __name__ == '__main__':
    main()