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
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        Integer[] x = new Integer[N];
        for (int i=0;i<N;i++) {
            x[i] = sc.nextInt();
        }
        int L = sc.nextInt();

        int[][] parent = new int[30][N];
        for (int i=0;i<N;i++) {
            parent[0][i] = ~Arrays.binarySearch(x, x[i]+L, (o1, o2)->o1>o2?1:-1)-1;
        }
        for (int j=0;j<29;j++) {
            for (int i=0;i<N;i++) {
                if (parent[j][i]!=N-1) {
                    parent[j+1][i] = parent[j][parent[j][i]];
                } else {
                    parent[j+1][i] = N-1;
                }
            }
        }
        // System.out.println(Arrays.deepToString(parent));
        int Q = sc.nextInt();
        for (int i=0;i<Q;i++) {
            int a = sc.nextInt()-1;
            int b = sc.nextInt()-1;
            if (a>b) {
                int tmp = a;
                a = b;
                b = tmp;
            }
            int ok = 1_000_000;
            int ng = -1;
            while (Math.abs(ok-ng)>1) {
                int mid = (ok+ng)/2;
                int tmp = a;
                for (int j=0;j<25;j++) {
                    if ((mid&(1<<j))==(1<<j)) {
                        if (tmp!=N) tmp = parent[j][tmp];
                    }
                }
                if (tmp>=b) {
                    ok = mid;
                } else {
                    ng = mid;
                }
            }
            System.out.println(ok);
        }
    }
}