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
N=int(input())
X=[int(x) for x in input().split()]
L=int(input())
inf=float("inf")
X.append(X[-1]+L)
Table=[[inf]*18 for i in range(N)]
r=1
for i in range(N):
  if r<=N:
    while X[r]-X[i]<=L:
      r+=1
      if r>N:
        break
  Table[i][0]=r-1
for k in range(1,18):
  for i in range(N):
    if Table[i][k-1]==N:
      Table[i][k]=N
      continue
    Table[i][k]=Table[Table[i][k-1]][k-1]

Q=int(input())
for q in range(Q):
  a,b=map(int,input().split())
  a-=1
  b-=1
  ans=0
  if a>b:
    a,b=b,a
  while a<b:
    i=bisect(Table[a],b)-1
    if i>=0:
      ans+=2**i
    else:
      ans+=1
    a=Table[a][i]
  
  print(ans)
