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())
x = list(map(int, input().split()))
L = int(input())
n = N.bit_length()+1
next_hotel = [[0]*n for _ in range(N)]
for i in range(N):
    index = bisect_right(x, x[i]+L)-1
    if index == i:
        next_hotel[i][0] = N
    else:
        next_hotel[i][0] = index
for i in range(1, n):
    for j in range(N):
        if next_hotel[j][i-1]<N:
            index = next_hotel[next_hotel[j][i-1]][i-1]
            if index == j:
                next_hotel[j][i] = N
            else:
                next_hotel[j][i] = index
        else:
            next_hotel[j][i] = N
def count(a, b):
    if a>b:
        a, b = b, a
    res = 0
    for i in range(n):
        if a >= b:
            return  res
        c = max(0, bisect_left(next_hotel[a], b)-1)
        a = next_hotel[a][c]
        res+=2**c
Q = int(input())
for _ in range(Q):
    a, b = map(int, input().split())
    print(count(a-1, b-1))