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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest._700problems
{
    class ARC060_E
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            List<int> xs = ReadInts().ToList();
            int l = ReadInt();
            int q = ReadInt();
            xs.Add(xs[xs.Count - 1] + l);
            int[][] abs = new int[q][];
            for(int i = 0; i < q; i++)
            {
                abs[i] = ReadInts();
                if (abs[i][0] > abs[i][1])
                {
                    int tmp = abs[i][0];
                    abs[i][0] = abs[i][1];
                    abs[i][1] = tmp;
                }
                abs[i][0]--;
                abs[i][1]--;
            }
            int top = 40;
            int[,] nexts = new int[n+1, top];
            int max = n;
            nexts[n, 0] = n;
            for (int i = n - 1; i >= 0; i--)
            {
                while (xs[max] - xs[i] > l)
                {
                    max--;
                }
                nexts[i, 0] = max;
            }
            for(int i = 1; i < top; i++)
            {
                for(int j = n ; j >= 0; j--)
                {
                    if (j == n)
                    {
                        nexts[j, i] = n ;
                    }
                    else
                    {
                        nexts[j, i] = nexts[nexts[j, i - 1], i - 1];
                    }
                }
            }
            for(int i = 0; i < q; i++)
            {
                int now = abs[i][0];
                long cnt = 0;
                while (now != abs[i][1])
                {
                    for(int j = top - 1; j >= 0; j--)
                    {
                        if (nexts[now,j] > abs[i][1]) continue;
                        cnt += (long)Pow(2, j);
                        now = nexts[now, j];
                        break;
                    }
                }
                WriteLine(cnt);
            }

        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}