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;

int main(){
  int N;
  cin>>N;
  vector<int> p(N);
  for(int i=0;i<N;i++){
    cin>>p[i];
  }
  int L;
  cin>>L;
  vector<vector<int>> dp(N,vector<int>(17));
  for(int j=0;j<17;j++){
    for(int i=0;i<N;i++){
      if(j==0){
        if(p[i]+L>=p[N-1]){
          dp[i][0]=N-1;
        }
        else{
          int b=lower_bound(p.begin(),p.end(),p[i]+L+1)-p.begin();
          dp[i][0]=b-1;
        }
      }
      else{
        dp[i][j]=dp[dp[i][j-1]][j-1];
      }
    }
  }
  int Q;
  cin>>Q;
  for(int l=0;l<Q;l++){
    int a,b;
    cin>>a>>b;
    a--,b--;
    if(a>b){
      swap(a,b);
    }
    int Z=1;
    for(int i=16;i>=0;i--){
      if(dp[a][i]<b){
        Z+=(1<<i);
        a=dp[a][i];
      }
    }
    cout<<Z<<endl;
  }
}