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>
using namespace std;
const int N=2e5;
int dep[N],f[20][N],fst[N],to[N],n,L,q,x[N],mm,sum[N];
int query(int l,int r)
{
	int ans=0;
	for(int i=17;i>=0;i--)if(f[i][l]&&f[i][l]<r)ans+=1<<i,l=f[i][l];
	return ans+(l!=r);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",x+i);
	scanf("%d%d",&L,&q);long long s=0;
	for(int i=1;i<=n;i++)sum[i]=sum[i-1]+x[i]-x[i-1];
	for(int i=1,j=2;i<n;i++)
	{
		while(s+x[j]-x[j-1]<=L&&j<=n)s+=x[j]-x[j-1],++j;
		f[0][i]=j-1;
		s-=x[i+1]-x[i];
	}
	for(int i=1;i<=17;i++)
		for(int j=1;j<=n;j++)
			f[i][j]=f[i-1][f[i-1][j]];
	for(int i=1;i<=q;i++)
	{
		int l,r;
		scanf("%d%d",&l,&r);if(l>r)swap(l,r);
		printf("%d\n",query(l,r));
	}
}