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;
typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1000000007;

int main() {
    ios::sync_with_stdio(false);
    int n, l, q, a[100005] = {}, h[18][100005] = {}, x, y;
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];
    cin >> l >> q;
    for (int i = 1; i <= n; i++) h[0][i] = (int)(upper_bound(a, a + n + 1, a[i] + l) - a) - 1;
    for (int i = 1; i <= 17; i++) for (int j = 1; j <= n; j++) h[i][j] = h[i - 1][h[i - 1][j]];
    while (q--) {
        cin >> x >> y;
        if (x > y) swap(x, y);
        int z = 0;
        while (h[0][x] < y) {
            for (int i = 1; i <= 17; i++) if (h[i][x] >= y) {z += (1 << (i - 1)); x = h[i - 1][x]; break;}
        }
        cout << z + 1 << '\n';
    }
}
