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>
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()
#define LL long long

using namespace std;

int main(){
    int N;cin>>N;
    int x[N];
    REP(i,N)cin>>x[i];
    LL L;cin>>L;
    int logN = (int)log2(N) + 1;

    int doub[N][logN+1];
    fill(doub[0],doub[N],x[N-1]+1);
    REP(i,N-1)doub[i][0]=upper_bound(x,x+N,x[i]+L)-x-1;
    REP(k,logN)REP(i,N)doub[i][k+1]=doub[min(N-1,doub[i][k])][k];

    int q;cin>>q;
    REP(i,q){
        int a,b;cin>>a>>b;
        if(a>b)swap(a,b);
        a--;b--;

        int ans=0;
        for(int i=logN-1;i>=0;i--){
            if(doub[a][i]<b){
                ans+= 1<<i;
                a = doub[a][i];
            }
        }
        cout<<ans+1<<endl;
    }
    return 0;
}