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 (
  "fmt"
)

func query(H *[]int, dest, sign int) {
  if dest * sign <= (*H)[0] * sign {
    fmt.Println(1)
    return
  }
  l := 0
  h := len(*H) - 1
  var m int
  for ; h - l > 1; {
    m = (h + l) / 2
    if (*H)[m] * sign < dest * sign {
      l = m
    } else {
      h = m
    }
  }
  fmt.Println(h + 1)
}

func main() {
  var N, L, Q int
  fmt.Scan(&N)
  X := make([]int, N)
  for i := range X {
    fmt.Scan(&X[i])
  }
  fmt.Scan(&L)
  H := make([][]int, N)
  RH := make([][]int, N)
  for i := range H {
    H[i] = make([]int, 0)
    RH[i] = make([]int, 0)
  }
  s := 0
  t := 0
  length := 0
  for ; s < N - 1; {
    for ; length <= L; t++{
      if t == N - 1 {
        for ; s < N - 1; s++ {
          H[s] = append(H[s], N - 1)
        }
        break
      }
      length += X[t + 1] - X[t]
    }
    for ; length > L; s++ {
      H[s] = append(H[s], t - 1)
      length -= X[s + 1] - X[s]
    }
  }
  length = 0
  for ; s > 0; {
    for ; length <= L; t-- {
      if t == 0 {
        for ; s > 0; s-- {
          RH[s] = append(RH[s], 0)
        }
        break
      }
      length += X[t] - X[t - 1]
    }
    for ; length > L; s-- {
      RH[s] = append(RH[s], t + 1)
      length -= X[s] - X[s - 1]
    }
  }
  for i := 1; i < N; i++ {
    H[N - 1 - i] = append(H[N - 1 - i], H[H[N - 1 - i][0]]...)
    RH[i] = append(RH[i], RH[RH[i][0]]...)
  }
  fmt.Scan(&Q)
  var a, b int
  for i := 0; i < Q; i++ {
    fmt.Scan(&a, &b)
    if a < b {
      query(&H[a - 1], b - 1, 1)
    } else {
      query(&RH[a - 1], b - 1, -1)
    }
  }
}