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<iostream>
#include<algorithm>
using namespace std;
int n,q,L,x[1<<17];
int d[20][1<<17];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)cin>>x[i];
	cin>>L;
	for(int i=0;i<n;i++)
	{
		d[0][i]=upper_bound(x,x+n,x[i]+L)-x-1;
	}
	for(int k=1;k<20;k++)
	{
		for(int i=0;i<n;i++)
		{
			d[k][i]=d[k-1][d[k-1][i]];
		}
	}
	cin>>q;
	for(;q--;)
	{
		int a,b;cin>>a>>b;
		a--,b--;
		if(a>b)swap(a,b);
		int ans=0;
		for(int k=20;k--;)
		{
			if(d[k][a]<b)
			{
				ans+=1<<k;
				a=d[k][a];
			}
		}
		cout<<ans+1<<endl;
	}
}