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.Linq;
using System.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var num = Input.num;
        var xs = Input.ar;
        var l = Input.num;
        var q = Input.num;
        var db = new int[num,20];
        for (var i = 0; i < num; i++)
            db[i, 0] = Search.UpperBound(xs, xs[i] + l) - 1;
        for (var i = num - 1; i >= 0; i--)
            for (var j = 1; j < 20; j++)
                db[i, j] = db[db[i, j - 1], j - 1];
        while (q-- > 0)
        {
            var ab = Input.ar;
            ab[0]--;ab[1]--;
            if (ab[0] > ab[1]) {
                var t = ab[0];
                ab[0] = ab[1];
                ab[1] = t;
            }
            var res = 0;
            while (ab[0] != ab[1])
            {
                for(var i=0;i<20;i++)
                    if(ab[1]<=db[ab[0],i])
                    {
                        if (i == 0) { res++;goto END; }
                        res += 1 << (i - 1);
                        ab[0] = db[ab[0], i-1];
                        break;
                    }
            }
            END:;
            WriteLine(res);
        }
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static char[][] gred(int h)
        => Enumerable.Repeat(0, h).Select(_ => read.ToCharArray()).ToArray();
    public static int[] ar1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => num).ToArray();
    public static long[] arL1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => numL).ToArray();
    public static string[] strs(int n)
        => Enumerable.Repeat(0, n).Select(_ => read).ToArray();
    public static int[][] ar2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => ar).ToArray();
    public static long[][] arL2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => arL).ToArray();
    public static List<T>[] edge<T>(int n)
        => Enumerable.Repeat(0, n).Select(_ => new List<T>()).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public static string[] Make<T1, T2>(out T1 v1, out T2 v2)
    {
        var r = read.Trim().Split(' ');
        v1 = getValue<T1>(r[0]);
        v2 = getValue<T2>(r[1]);
        return r;
    }
    public static string[] Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        var r = Make(out v1, out v2);
        v3 = getValue<T3>(r[2]);
        return r;
    }
    public static string[] Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        var r = Make(out v1, out v2, out v3);
        v4 = getValue<T4>(r[3]);
        return r;
    }
    public static string[] Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        var r = Make(out v1, out v2, out v3, out v4);
        v5 = getValue<T5>(r[4]);
        return r;
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}

public class Search
{
    public static int UpperBound<T>(IList<T> array,T value)
        where T : IComparable<T>
    {
        var low = 0;
        var high = array.Count;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) == 1) high = mid;
            else low = mid + 1;
        }
        return low;
    }
    
    public static int LowerBound<T>(IList<T> array,T value)
        where T : IComparable<T>
    {
        var low = 0;
        var high = array.Count;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) != -1) high = mid;
            else low = mid + 1;
        }
        return low;
    }

    public static T Max<T>(params T[] array)
        => array.Max();
    public static T Min<T>(params T[] array)
        => array.Min();
    public static bool Inside(int h, int w, int[] hw)
        => 0 <= h && h < hw[0] && 0 <= w && w < hw[1];
    public static bool IsPrime(long num)
    {
        if (num % 2 == 0 || num == 1) return num == 2;
        for (var i = 3L; i * i <= num; i += 2)
            if (num % i == 0) return false;
        return true;
    }

}