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<cstdio>
const int N=1e5+9;
int L[17][N],R[17][N],n,t,q,X[N],ans;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",X+i);
	scanf("%d",&t);
	for(int i=1,it=1;i<=n;++i){
		while(it<n&&X[it+1]-X[i]<=t)++it;
		R[0][i]=it;
	}
	for(int i=n,it=n;i;--i){
		while(it>1&&X[i]-X[it-1]<=t)--it;
		L[0][i]=it;
	}
	for(int i=1;i<17;++i)
	for(int j=1;j<=n;++j)
	R[i][j]=R[i-1][R[i-1][j]],L[i][j]=L[i-1][L[i-1][j]];
	for(scanf("%d",&q);q--;printf("%d\n",ans)){
		int x,y;ans=1;
		scanf("%d%d",&x,&y);
		if(x<=y){
			for(int i=16;~i;--i)
			if(R[i][x]<y)ans+=1<<i,x=R[i][x];
		}else{
			for(int i=16;~i;--i)
			if(L[i][x]>y)ans+=1<<i,x=L[i][x];
		}
	}
	return 0;
}