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=1e5+5;

int arr[N];
int dp[N][22];
int n,l,q;

int get(int a,int x)
{
	for(int i=21;i>=0;i--)
	{
		if(x&(1<<i))
			a=dp[a][i];
	}
	return a;
}

int main()
{
	cin >> n;
	for(int i=0;i<n;i++)
	{
		cin >> arr[i];
	}
	cin >> l >> q;
	int r=0;
	for(int i=0;i<n;i++)
	{
		if(r<i) r=i;
		while(r+1<n&&arr[r+1]-arr[i]<=l) r++;
		dp[i][0]=r;
	}
	for(int j=1;j<22;j++)
		for(int i=0;i<n;i++)
			dp[i][j]=dp[dp[i][j-1]][j-1];
	while(q--)
	{
		int a,b;
		cin >> a >> b;
		a--; b--;
		if(a>b) swap(a,b);
		int st=1,en=n,ans=n;
		while(st<=en)
		{
			int mid=(st+en)/2;
			//cout << a << " " << mid << " " << get(a,mid) << endl;
			if(get(a,mid)>=b)
			{
				ans=mid; en=mid-1;
			}
			else
				st=mid+1;
		}
		printf("%d\n",ans);
	}
}