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.*;
import java.lang.*;

class Main {

	public static void main(String[] args) {
		final Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] xs = new int[n];
		for (int i = 0; i < n; i++) {
			xs[i] = sc.nextInt();
		}

		int L = sc.nextInt();
		int num = 1;
		int t = 1;
		while (num < n) {
			num <<= 1;
			t++;
		}

		int[][] next = new int[t][n];
		for (int i = 0; i < n; i++) {
			next[0][i] = lowerBound(xs, xs[i] + L);
		}

		for (int k = 0; k < t - 1; k++) {
			for (int i = 0; i < n; i++) {
				next[k + 1][i] = next[k][next[k][i]];
			}
		}

		StringBuilder sb = new StringBuilder();
		int q = sc.nextInt();
		while (q-- > 0) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			if (a > b) {
				int c = a;
				a = b;
				b = c;
			}

			int answer = 1;
			for (int i = t - 1; i >= 0; i--) {
				if (xs[b] > xs[next[i][a]]) {
					a = next[i][a];
					answer += Math.pow(2, i);
				}
			}
			sb.append(answer).append("\n");
		}

		System.out.print(sb);
	}

	private static int lowerBound(int[] a, int x) {
		int l = 0, r = a.length;
		while (r - l > 1) {
			int m = (l + r) / 2;
			if (a[m] <= x) l = m;
			else r = m;
		}
		return l;
	}
}
