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
import bisect
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
d = int(input())
graph = [[0 for i in range(n+1)] for j in range(18)]
for i in range(n):
  x = bisect.bisect_right(a,a[i]+d)
  graph[0][i+1] = x
for j in range(1,18):
  for i in range(n):
    t = graph[j-1][i+1]
    graph[j][i+1] = graph[j-1][t]
q = int(input())
for _ in range(q):
  x,y = map(int,input().split())
  x,y = min(x,y),max(x,y)
  ans = 0
  for j in range(18)[::-1]:
    if graph[j][x] < y:
      ans += 2**j
      x = graph[j][x]
    if j == 0 and x < y:
      ans += 1
  print(ans)