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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <bitset>
#include <iostream>
typedef long long ll;
using namespace std;
const int maxn=101000;
int dis[maxn][35];
int n,l,q;
int num[maxn];
int main(){
    scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&num[i]);
	scanf("%d%d",&l,&q);
	for(int i=1;i<=n;i++){
		int idx=(int)(upper_bound(num+1,num+n+1,num[i]+l)-num);
		idx--;
		dis[i][0]=idx;
	}
	for(int j=1;j<=30;j++){
		for(int i=1;i<=n;i++){
			dis[i][j]=dis[dis[i][j-1]][j-1];
		}
	}
	while(q--){
		int a,b;
		scanf("%d%d",&a,&b);
		if(a==b){
			printf("0\n");
			continue;
		}
		if(a>b) swap(a,b);
		int ans=0,cur=a;
		for(int i=30;i>=0;i--){
			if(dis[cur][i]<b){
				ans+=(1<<i);
				cur=dis[cur][i];
			}
		}
		printf("%d\n",ans+1);
	}
	return 0;
}