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;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int r[20][101010];

int f(int s, int t, int x){
  int cur=s;
  rep(i,18) if((x>>i)&1){
    cur=r[i][cur];
  }
  if(cur>=t) return 1;
  else return 0;
}

int main(){
  int N;cin>>N;
  int X[N];
  rep(i,N) cin>>X[i];
  int L; cin>>L;
  rep(i,N){
    int x=upper_bound(X,X+N,X[i]+L)-X;
    r[0][i]=x-1;
  }
  rep(i,18) rep(j,N) r[i+1][j]=r[i][r[i][j]];
  int Q; cin>>Q;
  rep(i,Q){
    int a,b; cin>>a>>b; a--,b--;
    if(a>b) swap(a,b);
    int ok=N,ng=0;
    while(abs(ok-ng)>1){
      int mid=(ok+ng)/2;
      if(f(a,b,mid)) ok=mid;
      else ng=mid;
    }
    cout<<ok<<endl;
  }
  return 0;
}
