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 ll long long
#define rep(i,n) for(ll (i)=0;(i)<(n);++(i))
using namespace std;

int main(){
  ll n;
  cin>>n;
  ll logn=floor(log2(n));
  vector<ll> x(n);
  rep(i,n)cin>>x[i];
  ll l,q;
  cin>>l>>q;
  vector<vector<ll>> next(n,vector<ll>(logn+1));
  rep(i,n){
    next[i][0]=upper_bound(x.begin(), x.end(), x[i]+l)-1-x.begin();
  }
  rep(k,logn){
    rep(i,n){
      next[i][k+1]=next[next[i][k]][k];
    }
  }
  rep(i,q){
    ll a,b;
    cin>>a>>b;
    a--;b--;
    if(a>b)swap(a,b);
    ll ans=0;
    ll now=a;
    for(int k=logn;k>=0;k--){
      if(next[now][k]<b){
        now=next[now][k];
        ans+=(1<<k);
      }
    }
    cout<<ans+1<<endl;
  }
}

