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"
    "os"
    "strconv"
    "fmt"
    "container/heap"
)

const INF = 100000000000000


/*********** PriorityQueue ***********/
type PriorityQueue struct {
    arr []interface{}
    comp CompFunc
}

type CompFunc func(p, q interface{}) bool

func NewPriorityQueue() *PriorityQueue {
    return new(PriorityQueue)
}

func (pq PriorityQueue) Len() int {
    return len(pq.arr)
}

func (pq PriorityQueue) Swap(i, j int) {
    pq.arr[i], pq.arr[j] = pq.arr[j], pq.arr[i]
}

func (pq PriorityQueue) Less(i, j int) bool{
    return pq.comp(pq.arr[i], pq.arr[j])
}

func (pq *PriorityQueue) Push(x interface{}) {
    pq.arr = append(pq.arr, x)
}

func (pq *PriorityQueue) Pop() interface{} {
    n := pq.Len()
    item := pq.arr[n - 1]
    pq.arr = pq.arr[:n - 1]
    return item
}

func (pq *PriorityQueue) IsEmpty() bool {
    return pq.Len() == 0
}

/* type for edge */
type Edge struct {
    to int
    cost int
}

/* type for dijkstra */
type State struct {
    time int
    node int
}

/* dijkstra */

func dijkstra(start int, edges [][]Edge, n int, comp CompFunc) []int {
    var dist []int
    for i := 0; i < n; i++ {
        dist = append(dist, INF)
    }
    dist[start] = 0
    que := new(PriorityQueue)
    que.comp = comp
    heap.Push(que, State{time: 0, node:start})
    for !que.IsEmpty() {
        state := heap.Pop(que).(State)
        for _, edge := range edges[state.node] {
            newTime := state.time + edge.cost
            if dist[edge.to] > newTime {
                dist[edge.to] = newTime
                heap.Push(que, State{time: newTime, node: edge.to})
            }
        }
    }
    return dist
}
/* input */
var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
    sc.Scan()
    n, _ := strconv.Atoi(sc.Text())
    return n
}

func main() {
    sc.Split(bufio.ScanWords)
    n := readInt()
    var edges [][]Edge
    for i := 0; i < n; i++ {
        edges = append(edges, make([]Edge, 0))
    }
    for i := 0; i < n - 1; i++ {
        a, b, c := readInt() - 1, readInt() - 1, readInt()
        edges[a] = append(edges[a], Edge{to: b, cost: c})
        edges[b] = append(edges[b], Edge{to: a, cost: c})
    }

    var comp CompFunc
    comp = func(p, q interface{}) bool {
        return p.(State).time < q.(State).time
    }
    
    q, k := readInt(), readInt() - 1
    dist := dijkstra(k, edges, n, comp)
    wtr := bufio.NewWriter(os.Stdout)
    for i := 0; i < q; i++ {
        x, y := readInt() - 1, readInt() - 1
        //fmt.Println(dist[x] + dist[y])
        fmt.Fprintln(wtr, dist[x] + dist[y])
        //wtr.Flush()
    }
    wtr.Flush()
}