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: Accepted)

package main

import (
  "bufio"
  "fmt"
  "os"
  "strconv"
  "strings"
)

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()
  r := make([][]int,31)
  p := make([]int,31);p[0] = 1
  for k:=0;k<31;k++ { r[k] = make([]int,n+1) }
  for i:=1;i<n+1;i++ { r[0][i] = binarySearch(x,i,l) }
  for k:=0;k<30;k++ {
    p[k+1] = 2*p[k]
    for i:=1;i<n+1;i++ {
      r[k+1][i] = r[k][r[k][i]]
    }
  }
  for j:=0;j<q;j++ {
    a,b := input.NextInts()
    if a > b { a,b = b,a }
    inf,max := 0,b-a
    for max-inf > 1 {
      m := (max+inf)/2
      t := m
      s := a
      for k:=30;k>-1;k-- {
        if t < p[k] { continue }
        t -= p[k]
        s = r[k][s]
      }
      if s < b {
        inf = m
      } else {
        max = m
      }
    }
    fmt.Println(max)
  }
}
func binarySearch(x []int,i int,l int) int {
  sup,min := len(x),i
  for sup-min > 1 {
    m := (sup+min)/2
    if x[m] <= x[i]+l {
      min = m
    } else {
      sup = m
    }
  }
  return min
}

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
}