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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#define ll long long
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define max(p,q)((p)>(q)?(p):(q))

typedef struct edge{ll s,g,c;}E;
int edgehikaku(const void*a,const void*b){
	E*p=(E*)a,*q=(E*)b;
	if((*p).s<(*q).s)return -1;
	if((*p).s>(*q).s)return  1;
	if((*p).g<(*q).g)return -1;
	return 1;
}

E e[200010];
ll es[200010];
ll d[100010];
int n;

void dfs(int v,ll c){
	if(d[v])return;
	d[v]=c;
	for(int t=es[v];t<2*n-2&&e[t].s==v;t++)dfs(e[t].g,c+e[t].c);
}

int main(){
	scanf("%d",&n);
	rep(i,0,n-1){
		ll a,b,c;
		scanf("%lld%lld%lld",&a,&b,&c);
		a--;
		b--;
		e[i].s=e[i+n].g=a;
		e[i].g=e[i+n].s=b;
		e[i].c=e[i+n].c=c;
	}
	qsort(e,2*n-2,sizeof(E),edgehikaku);
	es[0]=0;
	ll t=0;
	rep(i,1,n){
		while(t<2*n-2&&e[t].s<i)t++;
		es[i]=t;
	}
	
	int q,k;
	scanf("%d%d",&q,&k);
	k--;
	dfs(k,1);
	while(q--){
		int a,b;
		scanf("%d%d",&a,&b);
		a--;
		b--;
		printf("%lld\n",d[a]+d[b]-2);
	}
	return 0;
}