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>
#include <algorithm>
#include <cmath>
#define N 100002
using namespace std;
int n,i,j,a[N],l,q,f[N][22];
int main()
{
	cin>>n;
	for(i=1;i<=n;i++) cin>>a[i];
	cin>>l>>q;
	for(i=1;i<=n;i++){
		int pos=lower_bound(a+1,a+n+1,a[i]+l)-a;
		if(a[pos]==a[i]+l) f[i][0]=pos;
		else f[i][0]=pos-1;
	}
	for(j=0;(1<<j)<=n;j++){
		for(i=1;i<=n;i++){
			if(f[i][j]==n) f[i][j+1]=0;
			else f[i][j+1]=f[f[i][j]][j];
		}
	}
	for(i=1;i<=q;i++){
		int x,y,ans=1<<30,tmp=0;
		cin>>x>>y;
		if(x>y) swap(x,y);
		for(j=log2(1.0*n);j>=0;j--){
			if(f[x][j]==0) continue;
			tmp+=pow(2,j);
			if(f[x][j]>=y){
				ans=min(ans,tmp);
				tmp-=pow(2,j);
			}
			else x=f[x][j];
		}
		cout<<ans<<endl;
	}
	return 0;
}
