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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func stringLineScan() string {
	sc.Scan()
	return sc.Text()
}

var comb [][]int

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, 1000000009)
	sc.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(stringLineScan())
	abc := make(map[int][][]int, n-1)
	for i := 0; i < n-1; i++ {
		x := make([][]int, 0)
		abc[i] = x
	}
	for i := 0; i < n-1; i++ {
		a, _ := strconv.Atoi(stringLineScan())
		b, _ := strconv.Atoi(stringLineScan())
		c, _ := strconv.Atoi(stringLineScan())
		a--
		b--
		p := make([]int, 2)
		p[0], p[1] = b, c
		abc[a] = append(abc[a], p)
		q := make([]int, 2)
		q[0], q[1] = a, c
		abc[b] = append(abc[b], q)
	}
	d := make([]int, n)
	for i := 0; i < n; i++ {
		d[i] = -1
	}
	q, _ := strconv.Atoi(stringLineScan())
	k, _ := strconv.Atoi(stringLineScan())
	k--
	d[k] = 0
	d = dist(k, abc, d)
	for i := 0; i < q; i++ {
		x, _ := strconv.Atoi(stringLineScan())
		y, _ := strconv.Atoi(stringLineScan())
		fmt.Println(d[x-1] + d[y-1])
	}
}
func dist(init int, abc map[int][][]int, d []int) []int {
	for _, i := range abc[init] {
		if d[i[0]] == -1 {
			d[i[0]] = d[init] + i[1]
			d = dist(i[0], abc, d)
		}
	}
	return d
}