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 <iostream>
#include <utility>
#include <algorithm>
#define inf 1000000007

using namespace std;

int N, L, Q;
int x[100005];
int Next[17][100005];

int main(void)
{
	cin >> N;
	for(int i = 0; i < N; i++) cin >> x[i];
	x[N] = x[N-1]+1;
	cin >> L;
	
	int p;
	for(int i = 0; i <= N; i++){
		Next[0][i] = upper_bound(x, x+N+1, x[i] + L) - x - 1;
	}
	for(int i = 1; i < 17; i++){
		for(int j = 0; j <= N; j++){
			Next[i][j] = Next[i-1][Next[i-1][j]];
		}
	}
	
	cin >> Q;
	int a, b;
	for(int q = 0; q < Q; q++){
		cin >> a >> b;
		a--, b--;
		if(a > b){
			int t = a;
			a = b, b = t;
		}
		
		int cur = a, ans = 0;
		for(int i = 16; i >= 0; i--){
			if(Next[i][cur] <= b){
				cur = Next[i][cur];
				ans += 1<<i;
			}
		}
		if(cur < b) ans++;
		cout << ans << endl;
	}
	
	return 0;
}