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>
using namespace std;
int n,l,q,x[110001],go[110001][19];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",x+i);
	scanf("%d%d",&l,&q);
	for(int i=1;i<=n;i++)go[i][0]=upper_bound(x+1,x+n+1,x[i]+l)-x-1;
	for(int i=1;i<19;i++)
		for(int j=1;j<=n;j++)go[j][i]=go[go[j][i-1]][i-1];
	while(q--)
	{
		int a,b,k=18,ans=0;
		scanf("%d%d",&a,&b);
		if(a>b)swap(a,b);
		while(a<b)
		{
			while(k&&go[a][k]>=b)k--;
			a=go[a][k];
			ans+=1<<k;
		}
		printf("%d\n",ans);
	}
}
