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.Text;


class A {
    int N;
    int maxN = 100005;
    int K;
    long L;
    int Q;
    long[] x;
    int[,] l;
    public A(){
        x = new long[maxN];
        l = new int[20,maxN];
    }
    public int calc(int a, int b){
        if(a==b) return 0;
        for(int i=0;i<K;i++){
            int h = (int)(1<<i);
            if(l[i,a]<=b && l[i+1,a]>b){
                return h+calc(l[i,a],b);
            }
        }
        return 0;
    }
    public string F(){
        return Console.ReadLine();
    }
    public void run(){
        N = int.Parse(F());
        string[] ss = F().Split(' '); 
        for(int i=0;i<N;i++){
            x[i] = long.Parse(ss[i]);
        }
        x[N] = x[N-1]+1;
        N = N+1;
        L = long.Parse(F());
        Q = int.Parse(F());
        
        K = (int)Math.Log(N,2)+3;
        
        int p = 1;
        for(int i=0;i<N;i++){
            while(p<N && x[p]-x[i] <= L) p++;
            p--;
            l[0,i] =  p;
        }
        
        for(int k=1;k<20;k++){
            for(int i=0;i<N;i++){
                l[k,i] = l[k-1,l[k-1,i]];
            }
        }
        
        StringBuilder sb = new StringBuilder("", 10*Q);
        for(int _=0;_<Q;_++){
            ss = F().Split(' '); 
            int a = int.Parse(ss[0])-1;
            int b = int.Parse(ss[1])-1;
            if(a>b){
                int tmp = a;
                a = b;
                b = tmp;
            }
            sb.Append(calc(a,b)+"\n");
        }
        Console.WriteLine(sb.ToString());
    }
}


class Program {
    static void Main(string[] args){
        A a = new A();
        a.run();    
    }
}