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: Wrong Answer)

# include <iostream>
# include <algorithm>
# include <vector>
# include <string>
# include <set>
# include <map>
# include <cmath>
# include <iomanip>
# include <functional>
# include <utility>
# include <stack>
# include <queue>
# include <list>
# include <tuple>
# include <unordered_map>
# include <numeric>
# include <complex>
# include <bitset>
# include <random>
# include <chrono>
using namespace std;
using LL = long long;
using ULL = unsigned long long;
typedef pair<LL, LL> P;
constexpr int INF = 2000000000;
constexpr int HINF = INF / 2;
constexpr double DINF = 100000000000000000.0;
constexpr long long LINF = 9223372036854775807;
constexpr long long HLINF = 4500000000000000000;
const double PI = acos(-1);
int dx[4] = { 0,1,0,-1 }, dy[4] = { 1,0,-1,0 };
# define ALL(x)      (x).begin(),(x).end()
# define UNIQ(c)     (c).erase(unique(ALL((c))),(c).end())
# define mp          make_pair
# define eb          emplace_back
# define FOR(i,a,b)  for(int i=(a);i<(b);i++)
# define RFOR(i,a,b) for(int i=(a);i>=(b);i--)
# define REP(i,n)    FOR(i,0,n)
# define INIT        std::ios::sync_with_stdio(false);std::cin.tie(0)

int n;
int x[101010];
int l, q;
int p[30][101010];

int main() {
	cin >> n;
	REP(i, n)cin >> x[i];
	cin >> l;
	x[n] = INF;
	REP(i, n+1) {
		p[0][i] = upper_bound(x, x + n+1, x[i] + l) - 1 - x;
	}
	for (int i = 1; i <= 16;i++) {
		REP(j, n+1) {
			p[i][j] = p[i-1][p[i-1][j]];
		}
	}
	int q;
	cin >> q;
	REP(i, q) {
		int a, b;
		cin >> a >> b;
		a--, b--;
		if (a > b)swap(a, b);
		int pos = a,ans = 0;
		for (int i = 16; i >= 0; i--) {
			if (p[i][pos] <= b) {
				pos = p[i][pos];
				ans += 1 << i;
			}
		}
		if (pos < b)ans++;
		cout << ans << endl;
	}
}