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.

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.

Example

Input

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5


Output

4
2
1
2
#include <bits/stdc++.h>
using namespace std;

const int N = 110000;

int go[17][N];

int main() {
	int n; cin >> n;
	vector<int> a(n + 1);
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
	}
	int L; cin >> L;
	for (int i = 1, j = 1; i <= n; i++) {
		while (j < n && a[j + 1] - a[i] <= L) j++;
		go[0][i] = j;
	}
	for (int i = 1; i < 17; i++) {
		for (int j = 1; j <= n; j++) {
			go[i][j] = go[i - 1][go[i - 1][j]];
		}
	}
	int q; cin >> q;
	while (q--) {
		int u, v; cin >> u >> v;
		if (u > v) swap(u, v);
		int ans = 0;
		for (int i = 16; i >= 0; i--) {
			if (go[i][u] >= v) continue;
			u = go[i][u];
			ans |= 1 << i;
		}
		ans++;
		cout << ans << "\n";
	}
	return 0;
}