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 <iostream>
#include <cstdio>
#define N 100005
using namespace std;
int n, l, q, x, y, k, s, a[N], b[N][20];
int main() {
	int i, j;
	scanf("%d", &n);
	for(i=1; i<=n; i++) scanf("%d", &a[i]);
	scanf("%d%d", &l, &q);
	for(i=j=1; i<n; i++) {
		for(; j<n && a[j+1]-a[i]<=l; j++);
		b[i][0] = j;
	}
	for(j=1; b[1][j-1]; j++) for(i=1; i<n; i++) {
		b[i][j] = b[b[i][j-1]][j-1];
	}
	k = j-2;
	while(q--) {
		scanf("%d%d", &x, &y);
		if(x>y) swap(x, y);
		for(j=k, s=0; j>=0; j--) {
			if(!b[x][j]) continue;
			if(b[x][j] < y) {
				s += 1<<j;
				x = b[x][j];
			}
		}
		printf("%d\n", s+1);
	}
	return 0;
}