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;

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

typedef long long ll;
typedef long double ld;

const int INF = 1e9;
const ld EPS = 1e-8;

int main(){
  int N, L, Q;
  cin >> N;
  vector<int> x(N);
  REP(i,N) cin >> x[i];
  cin >> L >> Q;

  vector<vector<int>> r(20, vector<int> (N));
  REP(i,N) {
    r[0][i] = upper_bound(ALL(x), x[i] + L) - x.begin() - 1;
  }
  REP(k,19)REP(i,N) r[k + 1][i] = r[k][r[k][i]];

  REP(i,Q) {
    int a, b;
    cin >> a >> b; --a; --b;
    if(a > b) swap(a, b);
    int res = 0;
    for(int j = 19; j >= 0; --j) {
      if(r[j][a] < b) {
        a = r[j][a];
        res += (1 << j);
      }
    }
    cout << res + 1 << endl;
  }
  return 0;
}

