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())
    xs = [int(c) for c in input().split()]
    l = int(input())

    xs.append(10 ** 17)
    nexts = list(range(n))
    for fr in range(n):
        p, q = fr, n
        while q - p > 1:
            m = (p + q) // 2
            if xs[m] - xs[fr] <= l:
                p = m
            else:
                q = m
        nexts[fr] = p

    doubling = [nexts]
    for _ in range(20):
        base = doubling[-1]
        nexts = [base[base_next] for base_next in base]
        doubling.append(nexts)

    def query(fr, to):
        if fr >= to:
            return 0
        p, q = 0, 20
        while q - p > 1:
            m = (p + q) // 2
            if doubling[m][fr] >= to:
                q = m
            else:
                p = m
        return query(doubling[p][fr], to) + 2 ** p

    q_count = int(input())
    for _ in range(q_count):
        a, b = map(int, input().split())
        if a > b:
            a, b = b, a
        a -= 1
        b -= 1

        print(query(a, b))


if __name__ == '__main__':
    main()