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 <algorithm>
using namespace std;

int N,L;
const int MAX_N = 100010;
int a[MAX_N],b[MAX_N][20];

void init(){
	a[N+1] = 2e9+1;
	for(int i=N,j=N+1;i>0;i--){
		while(a[i] + L < a[j])j--;
		b[i][0] = j;
	}
	for(int j=1;j<20;j++){
		for(int i=1;i<=N;i++){
			b[i][j] = b[b[i][j-1]][j-1];
		}
	}
}

int query(int x,int y){
	int ret = 0;
	for(int i=19;i>=0;i--){
		if(a[b[x][i]] < a[y]){
			x = b[x][i];
			ret += (1<<i);
		}
	}
	return ret+1;
}

int main(){
	ios::sync_with_stdio(false);
	cin >> N;
	for(int i=1;i<=N;i++){
		cin >> a[i];
	}
	cin >> L;

	init();

	int Q,x,y;
	cin >> Q;
	while(Q--){
		cin >> x >> y;
		if(x > y)swap(x,y);
		cout << query(x,y) << "\n";
	}
	return 0;
}