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>
int n,x[100100],L,f[100100][25],Q,l,r;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",&x[i]);
	scanf("%d",&L);
	int pre=n;
	for(int i=n,pre=n;i>=1;i--){
		while(x[i]+L<x[pre])pre--;
		f[i][0]=pre;
	}
	for(int i=1;i<=20;i++)
		for(int j=1;j<=n;j++){
			if(f[j][i-1]==n)f[j][i]=n;
			else f[j][i]=f[f[j][i-1]][i-1];
		}
	scanf("%d",&Q);
	while(Q--){
		scanf("%d%d",&l,&r);
		if(l>r)l^=r^=l^=r;
		int ans=0;
		for(int i=20;i>=0;)
			if(f[l][i]<r)ans+=1<<i,l=f[l][i];
			else i--;
		printf("%d\n",ans+1);
	}
} 