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>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#define SF scanf
#define PF printf
#define MAXN 100010
using namespace std;
typedef long long ll;
int n,m,q,u,v;
ll a[MAXN],l;
int go[MAXN][30];
int main(){
	SF("%d",&n);
	for(int i=1;i<=n;i++)
		SF("%d",&a[i]);
	int las=0;
	SF("%lld",&l);
	for(int i=1;i<=n;i++){
		while(a[i]-a[las]>l)	
			las++;
		go[i][0]=las;
	}
	for(int i=1;i<=n;i++)
		for(int j=1;j<=20;j++)
			go[i][j]=go[go[i][j-1]][j-1];
	SF("%d",&q);
	for(int i=1;i<=q;i++){
		SF("%d%d",&u,&v);
		if(u>v)
			swap(u,v);
		int len=20;
		int ans=0;
		while(u<v){
			while(len>0&&go[v][len]<u)
				len--;
			v=go[v][len];
			ans+=(1<<len);
		}
		PF("%d\n",ans);
	}
}