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"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}

var abc [200][200]int

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(os.Stdout)

	n := getNextInt(scanner)
	imm := IntMapMap{}

	for i := 0; i < n-1; i++ {
		a := getNextInt(scanner) - 1
		b := getNextInt(scanner) - 1
		c := getNextInt(scanner)
		imm.set(a, b, c)
		imm.set(b, a, c)
	}
	distance := make([]int64, n)
	color := make([]int, n)
	q := getNextInt(scanner)
	k := getNextInt(scanner) - 1

	queue := []int{k}
	color[k] = 1

	for len(queue) > 0 {
		p := queue[0]
		queue = queue[1:]
		for to, cost := range imm[p] {
			if color[to] != 0 {
				continue
			}
			color[to] = 1
			distance[to] = distance[p] + int64(cost)
			queue = append(queue, to)
		}
	}

	for i := 0; i < q; i++ {
		x := getNextInt(scanner) - 1
		y := getNextInt(scanner) - 1

		fmt.Fprintln(writer, distance[x]+distance[y])
	}

	writer.Flush()
}

// IntMap ...
type IntMap map[int]int

func (m IntMap) get(key int) int {
	if _, ok := m[key]; ok {
		return m[key]
	}
	return 0
}

func (m IntMap) set(key, n int) {
	if _, ok := m[key]; ok == false {
		m[key] = 0
	}
	m[key] = n
}

func (m IntMap) increment(key int) {
	if _, ok := m[key]; ok == false {
		m[key] = 0
	}
	m[key]++
}

// IntMapMap ...
type IntMapMap map[int]IntMap

func (m IntMapMap) get(key1, key2 int) int {
	if _, ok := m[key1][key2]; ok {
		return m[key1][key2]
	}
	return 0
}

func (m IntMapMap) set(key1, key2, n int) {
	if _, ok := m[key1]; ok == false {
		m[key1] = make(IntMap, 0)
	}
	m[key1].set(key2, n)
}

func (m IntMapMap) increment(key1, key2 int) {
	if _, ok := m[key1]; ok == false {
		m[key1] = make(IntMap, 0)
	}
	m[key1].increment(key2)
}