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>
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define FORR(i,a,b) for (int i=(a)-1;i>=(b);i--)
#define pb push_back

typedef long long ll;
using namespace std;
int MOD = 1000000007;
int N, L, Q;
map<int, int> m;
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> N;
  int tree[18][N], X[N];
  FOR(i, 0, N){
    int x;
    cin >> x;
    m[~x] = i;
    X[i] = ~x;
  }
  cin >> L >> Q;

  FOR(i, 0, N) tree[0][i] = m.lower_bound(X[i] - L) -> second;
  FOR(i, 1, 18) FOR(j, 0, N) tree[i][j] = tree[i-1][tree[i-1][j]];

  FOR(i, 0, Q){
    int a, b, s = 0;
    cin >> a >> b;
    if(a > b) swap(a, b);
    a -= 1;
    b -= 1;
    FORR(j, 18, 0){
      if(tree[j][a] < b){
        s += (1 << j);
        a = tree[j][a];
      }
    }
    cout << s+1 << "\n";
  }
}
