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;
long long f[100005][25];
long long arr[100005];
int main(){
	long long n,l,a,b,q;
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>arr[i];
	}
	cin>>l;
	for(int i=1;i<=n;i++){
		long long k=upper_bound(arr+1,arr+n+1,arr[i]+l)-arr;
		k=k-1;
		if(arr[i]+l>=arr[n]){
			f[i][0]=n;
		}
		else {
			f[i][0]=k;
		}
	}
	for(int j=1;j<=20;j++){
		for(int i=1;i<=n;i++){
			f[i][j]=f[f[i][j-1]][j-1];
		}
	}
	cin>>q;
	while(q--){
		cin>>a>>b;
		if(a>b)
			swap(a,b);
			long long ans=0;
			for(int i=20;i>=0;i--){
				if(f[a][i]<b){
					ans+=(1<<i);
					a=f[a][i];
				}
			}
			cout<<ans+1<<endl;
	}
}