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 maxn = 123456, lg = 20;
int a[maxn], p[lg][maxn];
int main(){
	int n; cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	int L; cin >> L;
	int j = 0;
	for(int i = 0; i < n; i++){
		while(j + 1 < n && a[j + 1] - a[i] <= L) j++;
		p[0][i] = j;
	}
	for(int i = 1; i < lg; i++){
		for(int j = 0; j < n; j++){
			p[i][j] = p[i - 1][p[i - 1][j]];
		}
	}
	int q; cin >> q;
	while(q--){
		int l, r; cin >> l >> r;
		if(l > r) swap(l, r);
		l--; r--;
		int ans = 0;
		for(int i = lg - 1; i >= 0; i--) if(p[i][l] < r) l = p[i][l], ans |= 1<<i;
		ans++;
		cout << ans << endl;
	}
	return 0;
}
