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 <stdio.h>
#include <algorithm>
using namespace std;

int N,L,Q,X[100006],J[100006][17];

int main()
{
	scanf ("%d",&N);
	for (int i=0;i<N;i++) scanf ("%d",&X[i]);
	scanf ("%d %d",&L,&Q);

	for (int i=0;i<N-1;i++) J[i][0] = upper_bound(X,X+N,X[i]+L) - X - 1;
	J[N-1][0] = N;
	for (int j=0;j<17;j++) J[N][j] = N;
	for (int i=N-1;i>=0;i--){
		for (int j=1;j<17;j++) J[i][j] = J[J[i][j-1]][j-1];
	}

	while (Q--){
		int a,b; scanf ("%d %d",&a,&b); a--; b--;
		if (a > b) swap(a,b);
		int s = 0;
		for (int i=16;i>=0;i--){
			if (J[a][i] < b) a = J[a][i], s += (1 << i);
		}
		s++;
		printf ("%d\n",s);
	}

	return 0;
}
