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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
static class Program{
	const int mod=1000000007;
	static void Main(){
		Sc sc=new Sc();
		int n=sc.I;
		int[] a=sc.Ia2;
		int l=sc.I;
		int[] tr=new int[n+1];
		int[] kr=new int[n+1];
		int m=n,t=0,b=0;
		for(int i = n-1;i>0;i--) {
			while(a[m]-a[i]>l){m--;}
			tr[i]=m;
			kr[i]=kr[m]+1;
			t=Math.Max(t,kr[i]);
		}
		m=1;
		while(m<t){m<<=1;b++;}
		int[][] h=new int[b][];
		h[0]=new int[n+1];
		for(int j = 0;j<=n;j++) {h[0][j]=tr[j];}
		h[0][n]=n;
		for(int i = 1;i<b;i++) {
			h[i]=new int[n+1];
			for(int j = 0;j<=n;j++) {
				h[i][j]=h[i-1][h[i-1][j]];
			}
		}
		int q=sc.I;
		int[] ans=new int[q];
		for(int i = 0;i<q;i++) {
			int[] e=sc.Ia;
			if(e[0]>e[1]){e[0]^=e[1];e[1]^=e[0];e[0]^=e[1];}
			int p=e[0],r=b-1;
			while(ans[i]==0){
				for(;r>=0;r--) {
					if(h[r][p]==e[1]){
						ans[i]=kr[e[0]]-kr[e[1]];
						break;
					}
					else if(h[r][p]<e[1]){
						p=h[r][p];
						r--;
						break;
					}
				}
				if(r==-1){
					ans[i]=kr[e[0]]-kr[h[0][p]];
					break;
				}
			}
		}
		Console.WriteLine("{0}",String.Join("\n",ans));
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
}