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
from bisect import bisect

n = int(input())
x = list(map(int, input().split()))
l = int(input())
q = int(input())

#r[i][j]: jから(2**i)日で行ける右端
r = [[i for i in range(n)] for _ in range(18)]
for j in range(n):
	r[0][j] = bisect(x, x[j]+l) - 1
for i in range(1, 18):
	for j in range(n):
		r[i][j] = r[i-1][r[i-1][j]]

def search(x, y):
	res = 0
	cur = x
	while True:
		for i in range(18):
			if r[i][cur] >= y:
				if i == 0:
					return res+1
				cur = r[i-1][cur]
				res += 1 << (i-1) 
				break

for _ in range(q):
	a, b = map(int, input().split())
	print(search(min(a, b)-1, max(a, b)-1))