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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Text;
using CompLib.Util;

public class Program
{
    private int N;
    private int[] X;
    private int L;
    private int Q;
    private int[] A, B;

    // iから2^j日で行けるホテル H[i][j]
    private List<int>[] Hotel;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        X = sc.IntArray();
        L = sc.NextInt();
        Q = sc.NextInt();
        A = new int[Q];
        B = new int[Q];
        for (int i = 0; i < Q; i++)
        {
            A[i] = sc.NextInt() - 1;
            B[i] = sc.NextInt() - 1;

            if (A[i] > B[i])
            {
                int t = A[i];
                A[i] = B[i];
                B[i] = t;
            }
        }

        Hotel = new List<int>[N];
        for (int i = N - 1; i >= 0; i--)
        {
            Hotel[i] = new List<int>();
            if (i == N - 1) continue;
            // 1日で行けるホテル
            int ok = i + 1;
            int ng = N;
            while (ng - ok > 1)
            {
                int mid = (ok + ng) / 2;
                if (X[mid] <= X[i] + L ) ok = mid;
                else ng = mid;
            }

            Hotel[i].Add(ok);
            int cur = ok;
            while (Hotel[i].Count <= Hotel[cur].Count)
            {
                int next = Hotel[cur][Hotel[i].Count - 1];
                Hotel[i].Add(next);
                cur = next;
            }
        }

        var sb = new StringBuilder();
        for (int i = 0; i < Q; i++)
        {
            // めんd
            int ng = 0;
            int ok = N;
            while (ok - ng > 1)
            {
                int mid = (ok + ng) / 2;
                if (C(A[i], mid) >= B[i]) ok = mid;
                else ng = mid;
            }

            sb.AppendLine(ok.ToString());
        }
        Console.Write(sb.ToString());
    }

    // ホテルbからd日で行けるホテル
    int C(int b, int d)
    {
        if (d == 0 || b == N - 1) return b;
        for (int i = Hotel[b].Count - 1; i >= 0; i--)
        {
            int p = 1 << i;
            if (p <= d) return C(Hotel[b][i], d - p);
        }

        throw new Exception();
    }

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            if (_index >= _line.Length)
            {
                string s;
                do
                {
                    s = Console.ReadLine();
                } while (s.Length == 0);

                _line = s.Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public string ReadLine()
        {
            _index = _line.Length;
            return Console.ReadLine();
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            string s = Console.ReadLine();
            _line = s.Length == 0 ? new string[0] : s.Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}