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;
#define N 100005

int n,x[N],l,le,ri,mid,t[20][N];
int q,a,b,ans,bates;

int main(){
	ios::sync_with_stdio(0); cin.tie(0);
	cin >> n;
	for (int i=1;i<=n;i++) cin >> x[i];
	cin >> l;
	for (int i=1;i<=n;i++){
		le=i; ri=n;
		while (le<=ri){
			mid=(le+ri)>>1;
			if (x[mid]<=x[i]+l){
				t[0][i]=mid; le=mid+1;
			}else ri=mid-1;
		}
	}
	for (int i=1;(1<<i)<=n;i++){
		for (int j=1;j<=n;j++)
		t[i][j]=t[i-1][t[i-1][j]];
	}
	for (;(1<<bates)<=n;bates++);
	bates--;
	cin >> q;
	while (q--){
		cin >> a >> b; ans=0;
		if (a>b) swap(a,b);
		for (int i=bates;i>=0;i--){
			if (i&&t[i-1][a]==t[i][a]||
			a==t[i][a]) continue;
			if (t[i][a]<b){
				ans+=(1<<i); a=t[i][a];
			}
		}
		cout << ans+1 << "\n";
	}
}