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;

inline int64_t in() { int64_t x = 0; cin >> x; return x; }

int main() {
  int n = in();

  vector<int> x(n);
  for (auto &i : x) cin >> i;

  int L = in();

  vector<vector<int>> d(20, vector<int>(n + 1, n));
  for (int i = 0; i < n; ++i) {
    d[0][i] = lower_bound(x.begin(), x.end(), x[i] + L + 1) - x.begin() - 1;
  }

  for (int i = 1; i < 20; ++i) {
    for (int j = 0; j < n; ++j) {
      d[i][j] = d[i - 1][d[i - 1][j]];
    }
  }

  int q = in();
  while (q--) {
    int a = in() - 1, b = in() - 1;
    if (b < a) swap(a, b);

    int ans = 1;
    for (int i = 19; i >= 0; --i) {
      if (d[i][a] < b) {
        ans += (1 << i);
        a = d[i][a];
      }
    }

    cout << ans << endl;
  }
}
