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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

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

    // Index[i][j] iから2^j日で行ける宿
    private List<int>[] Index;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        X = sc.IntArray();
        L = sc.NextInt();

        MkIndex();

        int Q = sc.NextInt();

        var sb = new StringBuilder();

        for (int i = 0; i < Q; i++)
        {
            sb.AppendLine(Query(sc.NextInt() - 1, sc.NextInt() - 1).ToString());
        }
        Console.Write(sb.ToString());
    }

    private int Query(int a, int b)
    {
        if (a > b)
        {
            int t = a;
            a = b;
            b = t;
        }
        int min = 0;
        int max = b - a;
        while (max-min > 1)
        {
            int med = (min + max) / 2;
            if (Calc(a, med) >= b)
            {
                max = med;
            }
            else
            {
                min = med;
            }
        }

        return max;
    }

    // iからd日で行けるとこ
    private int Calc(int i, int d)
    {
        if (d == 0) return i;
        int n = (int)Math.Log(d, 2);
        if (Index[i].Count <= n)
        {
            return N;
        }

        return Calc(Index[i][n], d - (1 << n));
    }

    private void MkIndex()
    {
        Index = new List<int>[N];

        for (int i = 0; i < N; i++)
        {
            Index[i] = new List<int>();
        }

        int sum = 0;
        int left = 1;
        for (int i = 1; i < N; i++)
        {
            sum += X[i] - X[i - 1];
            for (; sum > L; left++)
            {
                Index[left - 1].Add(i - 1);
                sum -= X[left] - X[left - 1];
            }
        }

        for (; left < N; left++)
        {
            Index[left - 1].Add(N - 1);
        }

        for (int i = 0;; i++)
        {
            bool flag = true;
            for (int j = 0; j < N; j++)
            {
                if (Index[j].Count >= i + 1 && Index[Index[j][i]].Count >= i + 1)
                {
                    Index[j].Add(Index[Index[j][i]][i]);
                    flag = false;
                }
            }
            if(flag)
                break;
        }
    }

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

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

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}