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 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<cstdio>
#include<cstring>
namespace fuck
{
	typedef long long ll;
	const int N=100100,M=N*2;
	int begin[N],next[M],to[M];
	ll w[M],dis[N];
	int n,m,e,root;
	void add(int x,int y,ll z,bool k=1)
	{
		to[++e]=y;
		next[e]=begin[x];
		begin[x]=e;
		w[e]=z;
		if(k)add(y,x,z,0);
	}
	void dfs(int p,int h=0)
	{
		for(int i=begin[p],q;i;i=next[i])
			if((q=to[i])!=h)
				dis[q]=dis[p]+w[i],dfs(q,p);
	}
	void initialize()
	{
		scanf("%d",&n);
		for(int i=1,u,v,h;i<n;i++)
			scanf("%d%d%d",&u,&v,&h),add(u,v,h);
		scanf("%d%d",&m,&root);
		dfs(root);
	}
	void solve()
	{
		initialize();
		for(int u,v;m--;)
		{
			scanf("%d%d",&u,&v);
			printf("%lld\n",dis[u]+dis[v]);
		}
	}
}
int main()
{
	fuck::solve();
	return 0;
}