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 = 1e5 + 5;

int n, L, q;
int a[N], nxt[18][N];

int main() {
	ios_base::sync_with_stdio(false);
	cin >> n;
	for (int i = 1; i <= n; ++i) cin >> a[i];
	
	cin >> L;
	int ptr = 1;
	for (int i = 1; i <= n; ++i) {
		while (ptr <= n && a[ptr] - a[i] <= L) ptr++;
		nxt[0][i] = ptr - 1;
	}
	
	for (int i = 1; i <= 17; ++i) {
		for (int j = 1; j <= n; ++j) {
			nxt[i][j] = nxt[i - 1][nxt[i - 1][j]];
		}
	}
	
	cin >> q;
	while (q--) {
		int u, v; cin >> u >> v;
		if (u > v) swap(u, v);
		int res = 1;
		for (int i = 17; i >= 0; --i) {
			if (nxt[i][u] < v) res += (1 << i), u = nxt[i][u];
		}
		cout << res << '\n';
	}
}