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
/*    三玖天下第一！！！  */
#include<bits/stdc++.h>
using namespace std;
const int ng=30,maxn=1e5;
int n,L,x[maxn+5]={},f[ng+5][maxn+5]={};
inline int dread()
{
	int x=0;bool f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f^=1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}
	return f?x:-x;
}
inline void in(){n=dread();for(int i=1;i<=n;i++) x[i]=dread();L=dread();}
inline void work()
{
	for(int i=1;i<=n;i++) f[0][i]=upper_bound(x+i,x+1+n,x[i]+L)-x-1;
	for(int i=1;i<=ng;i++) for(int j=1;j<=n;j++) f[i][j]=f[i-1][f[i-1][j]];
}
inline void out()
{
	for(int q=dread(),a,b,ans;q;q--)
	{
		a=dread();b=dread();ans=0;if(a>b) swap(a,b);
		for(int i=ng;i>=0;i--) if(f[i][a]<b) ans+=(1<<i),a=f[i][a];
		printf("%d\n",ans+1);
	}
}
int main(){in();work();out();return 0;}
