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

dp_plus = [[0]*(n+1) for i in range(30)]
dp_minus = [[0]*(n+1) for i in range(30)]

for i in range(n):
    now = x[i]
    reach = now + l
    dp_plus[0][i+1] = bisect_right(x, reach)

for i in range(n):
    now = x[i]
    reach = now - l
    dp_minus[0][i+1] = bisect_left(x, reach) + 1



for i in range(29):
    for j in range(1, n+1):
        dp_plus[i+1][j] = dp_plus[i][dp_plus[i][j]]
        dp_minus[i+1][j] = dp_minus[i][dp_minus[i][j]]


for _ in range(q):
    a, b = map(int, input().split())
    ans = 1
    if a < b:
        for i in range(29, -1, -1):
            if dp_plus[i][a] < b:
                a = dp_plus[i][a]
                ans += pow(2, i)

    else:
        for i in range(29, -1, -1):
            if dp_minus[i][a] > b:
                a = dp_minus[i][a]
                ans += pow(2, i)

    print(ans)
