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;

#define rep(i,l,r) for(int i=l;i<=r;++i)
#define per(i,r,l) for(int i=r;i>=l;--i)
const int N=1e5+5,L=17;
int a[N],f[N][L];

int main()
{
//	freopen("1.in","r",stdin);
	int n;
	cin>>n;
	rep(i,1,n)scanf("%d",a+i);
	int l;
	cin>>l;
	rep(j,0,L-1)f[n][j]=n;
	int now=n;
	per(i,n-1,1)
	{
		while(a[now]-a[i]>l)--now;
		f[i][0]=now;
		rep(j,1,L-1)f[i][j]=f[f[i][j-1]][j-1];
	}
	int m;
	cin>>m;
	while(m--)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		if(x>y)swap(x,y);
		int ans=0;
		per(j,L-1,0)
		if(f[x][j]<y)
		{
			ans+=1<<j;
			x=f[x][j];
		}
		printf("%d\n",ans+1);	
	}
}