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
#!/usr/bin/python3.6
import bisect
n = int(input())
x = [int(item) for item in input().split()]
l = int(input())
q = int(input())
ab = []
for i in range(q):
    a, b = [int(item) for item in input().split()]
    a -= 1; b -= 1
    if a > b:
        a, b = b, a
    ab.append((a, b))

dt = [[0] * n for _ in range(40)]
for i, item in enumerate(x):
    dt[0][i] = i
    dt[1][i] = bisect.bisect_right(x, item + l) - 1

for i in range(2, 40):
    for j in range(n):
        dt[i][j] = dt[i-1][dt[i-1][j]]

for a, b in ab:
    days = 0
    is_ok = False
    while a < b:
        for i in range(0, 40):
            if dt[i][a] >= b:
                if i == 1:
                    days += 1
                    is_ok = True
                else:
                    a = dt[i-1][a]
                    days += 2**(i-2)
                break
        if is_ok:
            break
    print(days)