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)

/*
これを入れて実行
g++ code.cpp
./a.out
*/

#include <iostream>
#include <vector>
#include <string>
#include <queue>
#include <deque>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
#include <cmath>
#include <math.h>
#include <tuple>
#include <iomanip>

using namespace std;
typedef long long ll;
typedef long double ld;

int dy4[4] = { -1, 0, +1, 0 };
int dx4[4] = { 0, +1, 0, -1 };
int dy8[8] = { -1, -1, 0, 1, 1, 1, 0, -1 };
int dx8[8] = { 0, 1, 1, 1, 0, -1, -1, -1 };

const long long INF = 1LL << 60;
const ll MOD = 1e9 + 7;

bool greaterSecond(const pair<int, int>& f, const pair<int, int>& s){
	return f.second > s.second;
}

ll gcd(ll a, ll b){
	if (b == 0)return a;
	return gcd(b, a % b);
}

ll lcm(ll a, ll b){
	return a / gcd(a, b) * b;
}

ll nCr(ll n, ll r){
	if (r == 0 || r == n){
		return 1;
	}
	else if (r == 1){
		return n;
	}
	return (nCr(n - 1, r) + nCr(n - 1, r - 1));
}

ll nPr(ll n, ll r){
	r = n - r;
	ll ret = 1;
	for (ll i = n; i >= r + 1; i--) ret *= i;
	return ret;
}

//-----------------------ここから-----------

class Edge{
public:
	ll to;
	ll dist;
};

ll n, q, k;

vector<vector<Edge>> g;

ll dist[100100] = { 0 };

bool visited[100100] = { false };

void dfs(int now){

	visited[now] = true;
	
	for (int i = 0; i < g[now].size(); i++){
		ll next = g[now][i].to;
		ll nextdist = g[now][i].dist;
		if (visited[next]){
			continue;
		}
		dist[next] = dist[now] + nextdist;
		dfs(next);
	}
}



int main(void){

	cin >> n;

	g.resize(n);

	

	for (int i = 0; i < n - 1; i++){
		ll a, b, c;
		cin >> a >> b >> c;
		a--;
		b--;
		Edge e1;
		e1.to = b;
		e1.dist = c;
		Edge e2;
		e2.to = a;
		e2.dist = c;
		g[a].push_back(e1);
		g[b].push_back(e2);
	}

	cin >> q >> k;

	k--;

	dfs(k);

	vector<pair<ll, ll>> l(q);

	for (int i = 0; i < q; i++){
		ll x, y;
		cin >> x >> y;
		x--;
		y--;
		l[i] = make_pair(x, y);
	}

	for (int i = 0; i < q; i++){
		cout << dist[l[i].first] + dist[l[i].second] << endl;
	}




}