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;

const int N = 1e5 + 5;
int n, x[N], jump[N][20], l, q;

int main () {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> x[i];
    cin >> l;

    for (int i = 1; i <= n; ++i) {
        int pos = upper_bound(x + 1, x + n + 1, x[i] + l) - x;
        jump[i][0] = pos - 1;
    }
    for (int j = 1; j < 20; ++j) {
        for (int i = 1; i <= n; ++i) {
            jump[i][j] = jump[ jump[i][j - 1] ][j - 1];
        }
    }
    cin >> q;
    while(q--) {
        int ans = 0, a, b; cin >> a >> b;
        if(a > b) swap(a, b);
        for (int i = 19; i >= 0; --i) if(jump[a][i] < b) ans += (1 << i), a = jump[a][i];
        cout << ans + 1 << '\n';
    }

    return 0;
}
