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 int long long
using namespace std;
const int N = 1e5+4;
vector <int> v;
int a[N];
int mx[N][25];
int len;
int n;
int jump(int x, int y)
{
	int ans = 0;
	for(int i=19;i>=0;i--)
	{
		if(mx[x][i] < y)
		{
			x = mx[x][i];
			ans += (1<<i);
		}
	}
 
	return ans+1;
}
 
signed main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",&a[i]);
	}
	cin>>len;
 
	for(int i=1;i<=n;i++)
	{
		mx[i][0] = lower_bound(a+1, a+1+n, a[i] + len + 1) - (a+1);
		// cout<<mx[i][0]<<'\n';
	}
 
 
	for(int j=1;j<=19;j++)
	{
		for(int i=1;i<=n;i++)
		{
			mx[i][j] = mx[mx[i][j-1]][j-1];
		}
	}
 
	int q;
	cin>>q;
	while(q--)
	{
		int i,j;
		scanf("%lld %lld",&i,&j);
		if(i > j)
			swap(i,j);
 
		cout<<jump(i,j)<<'\n';
	}
}