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 inpl(): return [int(i) for i in input().split()]
def hmd(a, b):
    ctr = -1
    while H[ctr+1][a] < b:
        ctr += 1
    vn = H[ctr][a]
    if (vn == b and ctr == 0) or ctr == -1:
        return 1
    return 2**ctr + hmd(vn,b)
N = int(input())
x = inpl() + [10**10]
L = int(input())
H = []
G = [N-1]*N
b = 0
for a in range(N):
    while x[b+1] - x[a] <= L:
        if b == N-1:
            break
        b += 1
    G[a] = b
H.append(G)
while G[0] != N-1:
    G = [G[i] for i in G]
    H.append(G)
H.append([10**10]*N)
Q = int(input())
for _ in range(Q):
    a, b = sorted(inpl())
    print(hmd(a-1,b-1))