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;
int n,l,q,a[100005],b[100005][21];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	scanf("%d",&l);
	int dem=1,sum=0;
	for(int i=2;i<=n;i++){
		sum+=a[i]-a[i-1];
		while(sum>l){
			b[dem][0]=i-1;
			dem++;
			sum-=(a[dem]-a[dem-1]);
		}
	}
	for(int i=dem;i<=n;i++){
		b[i][0]=n;
	}
	for(int j=1;(1<<j)<=n;j++){
		for(int i=1;i<=n;i++){
			b[i][j]=b[b[i][j-1]][j-1];
		}
	}
	scanf("%d",&q);
	while(q--){
		int u,v;
		scanf("%d %d",&u,&v);
		if(u>v) swap(u,v);
		int ans=1;
		for(int i=log2(n);i>=0;i--){
			if(b[u][i]<v){
				u=b[u][i];
				ans+=(1<<i);
			}
		}
		printf("%d\n",ans);
	}
}