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"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

func nextLine() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	i, _ := strconv.Atoi(nextLine())
	return i
}

func nextIntSplit() []int {
	splitted := strings.Fields(nextLine())
	n := len(splitted)
	res := make([]int, n)
	for i, str := range splitted {
		res[i], _ = strconv.Atoi(str)
	}
	return res
}

type edge struct {
	to   int
	cost uint
}

func dfs(graph [][]edge, costs []uint, node int, prev int, totalCost uint) {
	paths := graph[node]
	for _, p := range paths {
		if p.to != prev {
			cost := totalCost + p.cost
			costs[p.to] = cost
			dfs(graph, costs, p.to, node, cost)
		}
	}
}

func main() {
	n := nextInt()

	graph := make([][]edge, n+1)
	for i := 0; i < n-1; i++ {
		arr := nextIntSplit()
		a, b, cost := arr[0], arr[1], uint(arr[2])
		graph[a] = append(graph[a], edge{b, cost})
		graph[b] = append(graph[b], edge{a, cost})
	}

	qk := nextIntSplit()
	q, k := qk[0], qk[1]

	costs := make([]uint, n+1)
	dfs(graph, costs, k, -1, 0)

	for i := 0; i < q; i++ {
		q := nextIntSplit()
		fmt.Println(costs[q[0]] + costs[q[1]])
	}
}