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 C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cstdio>
#include <numeric>
#include <string>
#include <utility>
#include <vector>

int main() {
  int n, q, l, a, b;
  int x[100000];
  std::vector<std::vector<int>> next;
  std::scanf("%d", &n);
  for (int ni = 0; ni < n; ++ni) {
    std::scanf("%d", &x[ni]);
  }
  std::scanf("%d%d", &l, &q);
  next.resize(n, std::vector<int>(25));
  for (int ni = 0; ni < n; ++ni) {
    int inf = ni;
    int sup = n;
    while (sup - inf > 1) {
      int c = (inf + sup) / 2;
      if (x[c] <= x[ni] + l) {
        inf = c;
      } else {
        sup = c;
      }
    }
    next[ni][0] = inf;
  }
  for (int c = 1; c < 25; ++c) {
    for (int ni = 0; ni < n; ++ni) {
      next[ni][c] = next[next[ni][c - 1]][c - 1];
    }
  }
  for (int qi = 0; qi < q; ++qi) {
    int ans = 0;
    std::scanf("%d%d", &a, &b);
    if (a > b) {
      std::swap(a, b);
    }
    --a;
    --b;
    while (a < b) {
      for (int d = 24; true; --d) {
        if (d < 0) {
          return -1;
        }
        if (next[a][d] <= b) {
          a = next[a][d];
          ans += 1 << d;
          break;
        }
      }
    }
    std::printf("%d\n", ans);
  }
  return 0;
}