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 rep(i,x,y) for (int i=(x); i<=(y); i++)
#define ll long long
#define N 100005
using namespace std;
int n,q,L,a[N],f[N][20];
bool check(int x,int y,int z){
	rep (i,0,17) if (z>>i&1) x=f[x][i];
	return x>=y;
}
int main(){
	scanf("%d",&n);
	rep (i,1,n) scanf("%d",&a[i]);
	scanf("%d",&L);
	rep (i,1,n){
		int p=upper_bound(a+i,a+1+n,a[i]+L)-a; p--;
		f[i][0]=p;
	}
	rep (j,1,17) rep (i,1,n) f[i][j]=f[f[i][j-1]][j-1];
	scanf("%d",&q);
	while (q--){
		int x,y; scanf("%d%d",&x,&y);
		if (x>y) swap(x,y);
		int l=0,r=n,mid;
		while (l<=r){
			mid=l+r>>1;
			if (check(x,y,mid)) r=mid-1; else l=mid+1;
		}
		printf("%d\n",r+1);
	}
	return 0;
}