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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
	public Program() { }

	static void Main(string[] args)
	{
		new Program().prog();
	}
	Scanner cin;
	const int MOD = 1000000007;
	const int INF = int.MaxValue;
	const double EPS = 1e-7;
	const double PI = 3.1415926536;

	void prog()
	{
		cin = new Scanner();
		int[,] dir8 = new int[8, 2] { { -1, -1 }, { -1, 0 }, { -1, 1 }, { 0, -1 }, { 0, 1 }, { 1, -1 }, { 1, 0 }, { 1, 1 } };
		int[,] dir4 = new int[4, 2] { { -1, 0 }, { 0, -1 }, { 0, 1 }, { 1, 0 } };


		int N = cin.nextInt();
		int[] x = new int[N];
		for (int i = 0; i < N; i++)
		{
			x[i] = cin.nextInt();
		}
		int L = cin.nextInt();
		int Q = cin.nextInt();
		int[] a = new int[Q];
		int[] b = new int[Q];
		for (int i = 0; i < Q; i++)
		{
			a[i] = cin.nextInt() - 1;
			b[i] = cin.nextInt() - 1;
			if (a[i] > b[i])
			{
				int tmp = a[i];
				a[i] = b[i];
				b[i] = tmp;
			}
		}

		int depth = 16;
		int[,] r = new int[depth, N];
		for (int i = 0; i < N - 1; i++)
		{
			for (int j = i + 2; j < N; j++)
			{
				if (x[j] - x[i] > L)
				{
					r[0, i] = j - 1;
					break;
				}
			}
		}
		r[0, N - 2] = N - 1;
		r[0, N - 1] = N - 1;
		for (int i = 1; i < depth; i++)
		{
			for (int j = 0; j < N; j++)
			{
				r[i, j] = r[i - 1, r[i - 1, j]];
			}
		}
		for (int i = 0; i < Q; i++)
		{
			int ok = 16, ng = 0;
			while (ok - ng > 1)
			{
				int mid = (ok + ng) / 2;
				int now = a[i];
				int nowdepth = 0;
				while (mid > 0)
				{
					if ((mid & 1) == 1)
					{
						now = r[nowdepth, now];
					}
					nowdepth++;
					mid >>= 1;
				}
				if (now >= b[i])
				{
					ok = (ok + ng) / 2;
				}
				else
				{
					ng = (ok + ng) / 2;
				}
			}
			Console.WriteLine(ok);
		}
	}
}

class Scanner
{
	string[] s;
	int i;

	char[] cs = new char[] { ' ' };

	public Scanner()
	{
		s = new string[0];
		i = 0;
	}

	public string next()
	{
		if (i < s.Length) return s[i++];
		string st = Console.ReadLine();
		while (st == "") st = Console.ReadLine();
		s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
		i = 0;
		return next();
	}

	public int nextInt()
	{
		return int.Parse(next());
	}

	public long nextLong()
	{
		return long.Parse(next());
	}

	public double nextDouble()
	{
		return double.Parse(next());
	}
}