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;

int main() {
  int n; cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; ++i)
    cin >> v[i];

  int l; cin >> l;
  int j = n - 1;

  vector<vector<int>> go(20, vector<int>(n, -1));
  for (int i = n - 1; i >= 0; --i) {
    while (v[j] - v[i] > l) --j;
    go[0][i] = j;
    for (int k = 0; k < 19; ++k) {
      int nxt = go[k][i];
      if (nxt != -1)
        go[k + 1][i] = go[k][nxt];
    }
  }

  int q; cin >> q;
  while (q--) {
    int a, b; cin >> a >> b; --a; --b;
    if (a > b) swap(a, b);

    int ans = 1;
    for (int k = 19; k >= 0; --k) {
      if (go[k][a] == -1) continue;
      if (go[k][a] < b) {
        ans += (1 << k);
        a = go[k][a];
      }
    }
    cout << ans << '\n';
  }
  return 0;
}
