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(ll i = 0, i##_len = (n); i < i##_len; ++i)
#define all(n) begin(n), end(n)
using ll = long long;
using vl = vector<ll>;

int main() {
  ll n;
  cin >> n;
  vl x(n);
  rep(i, n) cin >> x[i];
  ll l, q;
  cin >> l >> q;
  vector<vl> r(20, vl(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(_, q) {
    ll a, b;
    cin >> a >> b;
    if(a > b) swap(a, b);
    a--;
    b--;
    ll ans = 1;
    for(ll k = 19; k >= 0; k--)
      if(r[k][a] < b) {
        a = r[k][a];
        ans += 1 << k;
      }
    cout << ans << '\n';
  }
}