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<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define int long long
const int N = 1e5 + 5;
const int M = 1e6 + 5;
const int mod = 1e9 + 7;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef set<int> si;
typedef map<string, int> msi;

int a[N], rmq[N][31];
signed main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int n; cin >> n;
	for(int i = 1 ; i <= n ; ++i) cin >> a[i];
	int d, q; cin >> d >> q;
	for(int i = 1 ; i <= n ; ++i)
		rmq[i][0] = (upper_bound(a + 1,a + n + 1, a[i] + d) - a - 1);
	for(int j = 1 ; j <= 20 ; ++j)
		for(int i = 1 ; i <= n ; ++i)
			rmq[i][j] = rmq[rmq[i][j - 1]][j - 1];
	for(int i = 1 ; i <= q ; ++i)
	{
		int u, v; cin >> u >> v;
		if(u > v) swap(u , v);
		int cnt = 0;
		for(int j = 20 ; j >= 0 ; --j)
		{
			if(rmq[u][j] < v)
			{
				cnt += (1 << j);
				u = rmq[u][j];
			}
		}
		cout << cnt + 1 << "\n";
	}
}