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 <cstdio>
#include <algorithm> 

const int MAXN = 1e5 + 1;

int n, l, q, x[MAXN];

int f[MAXN][31];
void prework() {
	for (int i = 1; i <= n; ++i) {
		int pos = std :: upper_bound(x + 1, x + n + 1, x[i] + l) - x - 1;
		f[i][0] = x[i] + l >= x[n] ? n : pos;
	}
	for (int j = 1; j <= 30; ++j) for (int i = 1; i <= n; ++i) f[i][j] = f[f[i][j - 1]][j - 1];
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) scanf("%d", &x[i]);
	scanf("%d%d", &l, &q);
	prework();
	while (q--) {
		int a, b; scanf("%d%d", &a, &b);
		if (a > b) std :: swap(a, b);
		int p = a, ans = 0;
		for (int j = 30; ~j; --j) if (f[p][j] < b) ans += (1 << j), p = f[p][j];
		printf("%d\n", ans + 1);
	}
	return 0;
}