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, L, Q;
    cin >> N;
    vector<int> X(N);
    for(int i=0; i<N; i++) cin >> X[i];
    cin >> L >> Q;

    vector<vector<int>> nxt(17, vector<int>(N));
    int r = 0;
    for(int l=0; l<N; l++){
        while(r<N && X[r]-X[l] <= L) r++;
        nxt[0][l] = r-1;
    }
    for(int k=1; k<17; k++) for(int i=0; i<N; i++) nxt[k][i] = nxt[k-1][nxt[k-1][i]];

    for(int i=0; i<Q; i++){
        int a, b;
        cin >> a >> b;
        a--; b--;
        if(a > b) swap(a, b);
        int ans = 0;
        for(int k=16; k>=0; k--) if(nxt[k][a] < b){
            ans += 1<<k;
            a = nxt[k][a];
        }
        cout << ans+1 << endl;
    }
}