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 N=100005;
int x[N],bk[17][N];
int main()
{
	int n,l,q;
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%d",x+i);
	scanf("%d%d",&l,&q);
	int pre=0;
	for(int i=0;i<n;i++)
	{
		while(x[i]-x[pre]>l)
			pre++;
		bk[0][i]=pre;
	}
	for(int i=1;i<17;i++)
		for(int j=0;j<=n;j++)
			bk[i][j]=bk[i-1][bk[i-1][j]];
	for(;q--;)
	{
		int a,b;
		scanf("%d%d",&a,&b);
		a--;
		b--;
		if(a==b)
		{
			puts("0");
			continue;
		}
		if(a>b)
			swap(a,b);
		int ret=0;
		for(int i=16;i>=0;i--)
		{
			if(bk[i][b]>a)
			{
				ret+=1<<i;
				b=bk[i][b];
			}
		}
		printf("%d\n",ret+1);
	}
	return 0;
}
