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: Runtime Error)

// Package main provides
//
// File:  d.go
// Author: ymiyamoto
//
// Created on Wed Jan  9 19:11:58 2019
//
package main

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

type graph [][]int

var lengths []int
var sc = bufio.NewScanner(os.Stdin)

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

func dfs(n int, g graph, length int) {
	lengths[n] = length

	for i := range g[n] {
		l := g[n][i]
		if l != 1<<60 {
			g[n][i] = 1 << 60
			g[i][n] = 1 << 60
			dfs(i, g, length+l)
		}
	}
}

func main() {
	var N int
	fmt.Scan(&N)

	g := make(graph, N)
	for i := range g {
		g[i] = make([]int, N)
		for j := range g[i] {
			g[i][j] = 1 << 60
		}
	}

	for i := 0; i < N-1; i++ {

		var a, b, c int

		fmt.Sscan(nextLine(), &a, &b, &c)
		g[a-1][b-1] = c
		g[b-1][a-1] = c
	}

	var Q, K int
	fmt.Scan(&Q, &K)

	lengths = make([]int, N)
	dfs(K-1, g, 0)

	for i := 0; i < Q; i++ {
		var x, y int
		fmt.Sscan(nextLine(), &x, &y)
		fmt.Println(lengths[x-1] + lengths[y-1])
	}
}