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.io.PrintWriter;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		int N = sc.nextInt();
		int[] x = new int[N];
		for(int i=0; i<N; i++)
			x[i] = sc.nextInt();
		int L = sc.nextInt();
		int Q = sc.nextInt();
		final int G = 18;
		int[][] m = new int[G][N];
		for(int i=0; i<N; i++) {
			int idx = Arrays.binarySearch(x, x[i]+L);
			if(idx<0)
				idx = -idx-2;
			m[0][i] = idx;
		}
		for(int i=1; i<G; i++) {
			for(int j=0; j<N; j++) {
				m[i][j] = m[i-1][m[i-1][j]];
			}
		}
		
		for(int i=0; i<Q; i++) {
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
			if(a>b) {
				int temp = a;
				a = b;
				b = temp;
			}
			int ans = 0;
			for(int j=G-1; j>=0; j--) {
				if(m[j][a]<b) {
					ans |= 1<<j;
					a = m[j][a];
				}
			}
			pw.println(ans+1);
		}
		
		sc.close();
		pw.close();
	}
	
}
