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,s,n) for(int i=s;i<n;++i)
#define rep(i,n) REP(i,0,n)

using namespace std;

typedef long long ll;

#define MAX 100010
ll N,Q,L;
ll x[MAX],a,b;

int nex[MAX][80];

void compute() {
  rep(i,N) {
    nex[i][0] = ( upper_bound(x,x+N,x[i]+L) - x ) - 1;
    assert( nex[i][0] != 0 );
  }

  rep(j,70) rep(i,N) nex[i][j+1] = nex[nex[i][j]][j];
  cin >> Q;
  rep(_,Q) {
    cin >> a >> b;
    --a, --b;
    if( !( a < b ) ) swap(a,b);
    ll cost = 0;
    for(int i=69;i>=0;--i) {
      if( nex[a][i] < b ) {
	cost += (1LL<<i);
	a = nex[a][i];
      }
    }
    cout << cost+1 << endl;
  }
}

int main() {
  cin >> N;
  rep(i,N) cin >> x[i];
  cin >> L;
  compute();
  return 0;
}
