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 maxn=1e5+10;
int n,a[maxn],l,q;
int f[maxn][31];
int main()
{
	ios::sync_with_stdio(0);
    cin.tie(0);
	cout.tie(0);		
    cin>>n;
    for (int i=1; i<=n; i++) cin>>a[i];
    cin>>l;
    for (int i=1;i<=n;i++)
	{
        int idx=upper_bound(a+1,a+1+n,a[i]+l)-a-1;
        if(a[i]+l>=a[n]) f[i][0]=n;
        else f[i][0]=idx;
    }
    for (int j=1; j<=30; j++)
       for (int i=1;i<=n;i++)
            f[i][j]=f[f[i][j-1]][j-1];
    cin>>q;
    while(q--){
        long long u,v;
        cin>>u>>v;
        if(u>v) swap(u,v);
        long long dem;
        dem=0;
        for(int i=30;i>=0;i--)
          if(f[u][i]<v)
             {
             	dem+=(1<<i);
             	u=f[u][i];
			 }
        cout<<dem+1<<endl;
    }
}
