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: Time Limit Exceeded)

#include <iostream>
#include <climits>
#include <stack>
#include <queue>
#include <string>
#include <random>
#include <utility>
#include <string.h>
#include <iomanip>
#include <stdlib.h>
#include <algorithm>
using namespace std;
typedef pair<int,int> P;
long long int INF = 1e18;
double Pi = 3.141592653589;
const int mod = 1000000007;
// memset(a,0,sizeof(a)); →全部０にする
 
long long int i,j;
int n;
long long int a[100005],b[100005],c[100005];
int q,k,xxx;
int x[100005],y[100005];
long long int d[100005];


void dfs(int node,long long int p){
	for(int i=1;i<=n;i++){
		if(d[a[i]]==INF && d[b[i]]==INF)continue;
		if(a[i]==node && d[b[i]]==INF){
			d[b[i]] = p + c[i];
			dfs(b[i],p+c[i]);
		}else if(b[i]==node && d[a[i]]==INF){
			d[a[i]] = p+c[i];
			dfs(a[i],p+c[i]);
		}
	}
	return;
}
int main(){
	cin>>n;
	for(i=1;i<=n-1;i++){
		cin>>a[i]>>b[i]>>c[i];
	}
	cin>>q>>k;
	for(i=1;i<=q;i++){
		cin>>x[i]>>y[i];
	}
	for(i=1;i<=n;i++){
		d[i]=INF;
	}
	d[k]=0;
	//d[i]:iからKまでの距離
	bool flag = false;
	dfs(k,0);
	int xx,yy;
	for(i=1;i<=q;i++){
		cout<<d[x[i]]+d[y[i]]<<endl;
	}
	return 0;
}