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>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
long long n,m,q,i,j,dp[1<<18][18],l,r,x,y,ans,now,wx[100005];
int main()
{
	ios::sync_with_stdio(0);
	cin>>n;
	for (i=1;i<=n;i++) cin>>wx[i];
	cin>>m;
	for (i=1;i<=n;i++)
	{
		while (j<n&&wx[i]+m>=wx[j+1]) j++;
		dp[i][0]=j;
	}
	for (j=1;j<=17;j++)
	{
		for (i=1;i<=n;i++)
		{
			dp[i][j]=dp[dp[i][j-1]][j-1];
		}
	}
	cin>>q;
	for (i=1;i<=q;i++)
	{
		cin>>l>>r;
		if (l>r) swap(l,r);
		ans=0;
		for (j=17;j>=0;j--)
		{
			while (dp[l][j]<r)
			{
				l=dp[l][j];
				ans+=1<<j;
			}
		}
		cout<<ans+1<<endl;
	}
	return 0;
}