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>
#define N 100010
#define swap(a,b) a^=b^=a^=b
using namespace std;
int l,n,m;
int k=2;
int f[N][32]={},a[N]={};
int read(){int s=0,w=1;char ch=getchar();while((ch>'9'||ch<'0')&&ch!='-')ch=getchar();if(ch=='-')w=-1;while(ch<='9'&&ch>='0')s=s*10+ch-'0',ch=getchar();return s*w;}
int main()
{
		n=read();
		for(int i=1;i<=n;++i)a[i]=read();
		l=read();
		for(int i=1;i<=n;++i)
		{
			while(k<=n&&a[k]-a[i]<=l)++k;
			f[i][0]=k-1;
		}
		for(int i=1;i<=30;++i)
			for(int j=1;j<=n;++j)
				f[j][i]=f[f[j][i-1]][i-1];
		m=read();
		for(int i=1;i<=m;++i){
				int x,y;
				int ans=0;
				x=read();y=read();
				if(x>y)swap(x,y);
				for(int j=30;j>=0;--j){
						if(f[x][j]>=y)continue;
						ans+=1<<j,x=f[x][j];
				}
				printf("%d\n",ans+1);
		}
		return 0;
}
