Problem:
Score : 700 points

Problem Statement

N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.

Tak the traveler has the following two personal principles:

He never travels a distance of more than L in a single day.

He never sleeps in the open. That is, he must stay at a hotel at the end of a day.

You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j.
For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.
It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.

Constraints

2 \leq N \leq 10^5

1 \leq L \leq 10^9

1 \leq Q \leq 10^5

1 \leq x_i < x_2 < ... < x_N \leq 10^9

x_{i+1} - x_i \leq L

1 \leq a_j,b_j \leq N

a_j \neq b_j

N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.

Partial Score

200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q

Output

Print Q lines.
The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.

Sample Input 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

4
2
1
2

For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:

Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.

Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.

Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.

Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.

Solution in Go (1.6) (judge verdict: Runtime Error)

package main

import (
  "bufio"
  "container/heap"
  "fmt"
  "os"
  "sort"
  "strconv"
  "strings"
)

const INF int = 100000000

func main() {
  input := Input{bufio.NewReaderSize(os.Stdin,1000000)}
  n := input.NextInt()
  x := append(append([]int{0},input.NextIntArray()...),2100000000)
  l := input.NextInt()
  q := input.NextInt()
  u := make([]int,n+1)
  g := NewGraph(n+1)
  for i:=1;i<n+1;i++ {
    j := sort.Search(n+2,func(j int) bool { return x[i]+l < x[j] })
    if u[i] == 0 { u[i] = i }
    if u[j-1] == 0 { u[j-1] = u[i] }
    g.Add(i,j-1,1)
  }
  c := make([][]int,n+1)
  for i:=1;i<n+1;i++ {
    if u[i] == i { c[i] = g.Dijkstra(i) }
  }
  for k:=0;k<q;k++ {
    a,b := input.NextInts()
    if a > b { a,b = b,a }
    fmt.Println(c[u[a]][b]-c[u[a]][a])
  }
}

type Item struct { pos,cost,idx int }
type PriorityQueue []*Item
func(pq PriorityQueue) Len() int { return len(pq) }
func(pq PriorityQueue) Less(i,j int) bool { return pq[i].cost < pq[j].cost }
func(pq PriorityQueue) Swap(i,j int) {
  pq[i],pq[j] = pq[j],pq[i]
  pq[i].idx,pq[j].idx = i,j
}
func(pq *PriorityQueue) Push(x interface{}) {
  n := len(*pq)
  item := x.(*Item)
  item.idx = n
  *pq = append(*pq,item)
}
func(pq *PriorityQueue) Pop() interface{} {
  old := *pq
  n := len(old)
  item := old[n-1]
  item.idx = -1
  *pq = old[0:n-1]
  return item
}
 
type Edge struct { to,cost int }
type Graph [][]Edge
func NewGraph(n int) Graph { return make([][]Edge,n) }
func(g Graph) AddEdge(from int,e Edge) { g[from] = append(g[from],e) }
func(g Graph) Add(from,to,cost int) { g.AddEdge(from,Edge{to,cost}) }
func(g Graph) Dijkstra(start int) []int {
  n := len(g)
  c := make([]int,n)
  for i:=0;i<n;i++ { c[i] = INF }
  var pq PriorityQueue
  heap.Init(&pq)
  heap.Push(&pq,&Item{pos:start,cost:0})
  c[start] = 0
  for pq.Len() > 0 {
    s := heap.Pop(&pq).(*Item)
    if s.cost > c[s.pos] { continue }
    for _, e := range g[s.pos] {
      if c[e.to] > s.cost+e.cost {
        c[e.to] = s.cost+e.cost
        heap.Push(&pq,&Item{pos:e.to,cost:c[e.to]})
      }
    }
  }
  for i:=n-2;i>-1;i-- {
    if c[i] == INF { c[i] = c[i+1] }
  }
  return c
}

type Input struct { reader *bufio.Reader }
func(i *Input) NextLine() string {
  var buffer []byte
  for {
    line,isPrefix,err := i.reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer,line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func(i *Input) NextInt() int {
  n,_ := strconv.Atoi(i.NextLine())
  return n
}
func(i *Input) NextInts() (int,int) {
  s := strings.Split(i.NextLine()," ")
  x,_ := strconv.Atoi(s[0])
  y,_ := strconv.Atoi(s[1])
  return x,y
}
func(i *Input) NextIntArray() []int {
  s := strings.Split(i.NextLine()," ")
  a := make([]int,len(s))
  for i:=0;i<len(s);i++ { a[i],_ = strconv.Atoi(s[i]) }
  return a
}