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 PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
list($n) = ints();
$dk = new Dijkstra($n);
for ($i = 0; $i < $n - 1; ++$i) {
    list($a, $b, $c) = ints();
    --$a;
    --$b;
    $dk->connect($a, $b, $c);
    $dk->connect($b, $a, $c);
}
list($q, $k) = ints();
--$k;
$dk->solve($k);
for ($i = 0; $i < $q; ++$i) {
    list($x, $y) = ints();
    --$x;
    --$y;
    $ans[] = $dk->dist($k, $x) + $dk->dist($k, $y);
}
echo implode(PHP_EOL, $ans);

function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}

class Dijkstra
{
    private $n;
    private $d; // 最短距離を格納
    private $cost; // ノード間の距離を格納
    private $root; // 最短経路を格納

    function __construct($n)
    {
        $this->n = $n;
        $this->cost = array_fill(0, $this->n, array_fill(0, $this->n, INF));
    }

    function connect($x, $y, $w)
    {
        $this->cost[$x][$y] = $w;
    }

    function solve($s = 0)
    {
        $this->d[$s] = array_fill(0, $this->n, INF);
        $this->d[$s][$s] = 0;
        $this->root[$s] = array_fill(0, $this->n, [$s]); // 各ノードまでの最短経路を格納
        $used = array_fill(0, $this->n, false);
        while (true) {
            $v = -1;
            // 残りのノードのうち最短で到達出来るノードを選択
            for ($i = 0; $i < $this->n; ++$i) {
                if (!$used[$i] && $v === -1) $v = $i;
                elseif (!$used[$i] && $this->d[$s][$i] < $this->d[$s][$v]) $v = $i;
            }
            if ($v === -1) break;
            for ($i = 0; $i < $this->n; ++$i) {
                if ($this->d[$s][$i] > $this->d[$s][$v] + $this->cost[$v][$i]) {
                    $this->d[$s][$i] = $this->d[$s][$v] + $this->cost[$v][$i];
                    $this->root[$s][$i] = array_merge($this->root[$s][$v], [$i]);
                }
            }
            $used[$v] = true;
        }
    }

    function dist($x, $y)
    {
        return $this->d[$x][$y];
    }

    function root($x, $y)
    {
        return $this->root[$x][$y];
    }
}