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_left, bisect_right

N = int(input())
xs = list(map(int, input().split()))
L = int(input())
Q = int(input())
ABs = [tuple(map(lambda x: int(x)-1, input().split())) for _ in range(Q)]

logN = ((N-1).bit_length())
parentss = [[N-1]*(logN+1) for _ in range(N)]
for i in range(N-1):
    iL = bisect_right(xs, xs[i]+L)
    parentss[i][0] = iL-1

for d in range(1, logN+1):
    for i in range(N-1):
        parentss[i][d] = parentss[parentss[i][d-1]][d-1]

anss = []
for A, B in ABs:
    if A > B:
        A, B = B, A
    i = A
    ans = 1
    for d in reversed(range(logN+1)):
        if parentss[i][d] < B:
            i = parentss[i][d]
            ans += 2**d
    anss.append(ans)

print('\n'.join(map(str, anss)))
