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
def main():
    n = int(input())
    x = list(map(int, input().split()))
    l = int(input())
    q = int(input())
    ab = [list(map(lambda x:int(x)-1, input().split())) for _ in [0]*q]
    doubling = [[] for _ in [0]*n]
    j = 0
    for i in range(n):
        while j < n:
            if x[j]-x[i] > l:
                doubling[i].append(j-1)
                break
            else:
                j += 1
    for i in range(n-1, -1, -1):
        if not doubling[i]:
            doubling[i].append(n-1)
        else:
            break
    for _ in range(16):
        for i in range(n):
            doubling[i].append(doubling[doubling[i][-1]][-1])
    for a, b in ab:
        if a > b:
            a, b = b, a
        ans = 0
        j = 16
        while j >= 0:
            if doubling[a][j] >= b:
                j -= 1
            else:
                a = doubling[a][j]
                ans += 2**j
        if a == b:
            print(ans)
        else:
            print(ans+1)


main()
