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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

int N, L, Q;
int X[100000];
int U[19][100000];

int main() {
  cin >> N;
  for (int i=0; i<N; i++) cin >> X[i];
  cin >> L >> Q;
  for (int i=N-1; i>=0; i--) {
    U[0][i] = min((int)(upper_bound(X, X+N, X[i]+L) - X - 1), N-1);
    for (int k=0; k<18; k++) {
      U[k+1][i] = U[k][U[k][i]];
    }
  }
  for (int i=0; i<Q; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    if (a > b) swap(a, b);
    int c = 1;
    for (int k=18; k>=0; k--) {
      if (U[k][a] < b) {
        a = U[k][a];
        c += (1<<k);
      }
    }
    cout << c << "\n";
  }
  return 0;
}
