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<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int parse[100010][21];
int n;
int a[100010];
int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
	{
		scanf("%d", &a[i]);
	}
	a[n+1] = 1234567890;
	int q;
	scanf("%d", &q);
	for (int i = 1; i <=n; i++)
	{
		int t = upper_bound(a, a + n+1, a[i] + q) - a;
		parse[i][0] = t - 1;
	}
	for (int i = 1; i < 21; i++)
	{
		for (int y = 1; y <=n; y++)
			parse[y][i] = parse[parse[y][i - 1]][i - 1];
	}
	int o;
	scanf("%d", &o);
	while (o--)
	{
		int w, e;
		scanf("%d %d", &w, &e);
		if (w > e)
			swap(w, e);
		int dap = 0;
		for (int i = 20; i >= 0; i--)
		{

			if (parse[w][i] == 0)continue;
			if (parse[w][i] < e)
			{
				dap += (1 << i);
				w = parse[w][i];
			}
		}
		dap++;
		printf("%d\n", dap);
	}
}