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 C++14 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

//============================================================================
// Name        : abc70d.cpp
// Author      : 
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================
#include<algorithm>
#include<iostream>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<cmath>
#include<list>
#include<set>
#include<map>

using namespace std;

map<int, bool> mp;
void dfs(vector<vector<pair<int, long long>>> &A, vector<long long> &dist, int n){
	mp[n] = 1;
	for(int i = 0; i < A[n].size(); ++i){
		dist[A[n][i].first] = min(dist[n] + A[n][i].second, dist[A[n][i].first]);
		if(mp[A[n][i].first] == 0)dfs(A, dist, A[n][i].first);
	}

	mp[n] = 0;
}

int main() {
	int N;
	cin >> N;
	vector<vector<pair<int, long long>>> A(N + 1);
	for(int i = 0; i < N - 1; ++i){
		int a, b;
		long long c;
		scanf("%d %d %lld", &a, &b, &c);
		A[a].push_back(make_pair(b, c));
		A[b].push_back(make_pair(a, c));
	}

	int Q, K;
	cin >> Q >> K;

	vector<long long> dist(N + 1, 1ll << 62);
	dist[K] = 0;
	for(int i = 0; i < A[K].size(); ++i){
		dist[A[K][i].first] = min(dist[A[K][i].first] + A[K][i].second, A[K][i].second);
		dfs(A, dist, A[K][i].first);
	}

	vector<int> a(Q), b(Q);
	for(int i = 0; i < Q; ++i){
		scanf("%d %d", &a[i], &b[i]);
		printf("%lld\n", dist[a[i]] + dist[b[i]]);
	}

	return 0;
}