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>
#define INF 100000
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;

int x[100000];
int r[18][100000];
int main() {
	int n; scanf("%d", &n);
	rep(i, n)scanf("%d", &x[i]);
	int l, q; scanf("%d%d", &l, &q);
	rep(i, n)r[0][i] = upper_bound(x, x + n, x[i] + l) - x - 1;
	for (int i = 1; i < 18; i++) {
		rep(j, n)r[i][j] = r[i - 1][r[i - 1][j]];
	}
	rep(i, q) {
		int a, b; scanf("%d%d", &a, &b); a--; b--;
		if (a > b)swap(a, b);
		int lb = 0, rb = INF;
		while (lb != rb) {
			int t = (lb + rb) / 2;
			int e = a, f = b;
			for (int i = 17; i >= 0; i--) {
				if (t >> i & 1)e = r[i][e];
			}
			if (e >= f)rb = t;
			else lb = t + 1;
		}
		printf("%d\n", lb);
	}
}