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;
const int N = 1e5+50;
const int oo = 22;
int n, d, q;
int a[N];
map<int,int > M;
int P[N][oo];
signed main(){
	cin >> n;
	for(int i=1;i<=n;i++) cin >> a[i];
	cin >> d;
	for(int i=1;i<=n;i++){
		int v = a[i] + d;
		int k = lower_bound(a+1,a+n+1,v) - a;
		if(a[k]>v||k==n+1)	k--;
		P[i][0] = k;
	}
	for(int j=1;(1<<j)<=n;j++){
		for(int i=1;i<=n;i++){
			P[i][j] = P[P[i][j-1]][j-1];
		}
	}
	
	cin >> q;
	while(q--){
		int u, v;
		cin >> u >> v;
		if(u>v) swap(u,v); 
		int lg = log2(n);
		int ans = 0;
		for(int i=lg;i>=0;i--){
			if(P[u][i]<v){
				u = P[u][i];
				ans+=(1<<i);
			}
		}
		cout << ans+1 << endl;
	}
}