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 math
N = int(input())
x = list(map(int, input().split()))
L = int(input())

m = int(math.log(max(x), 2) + 1)
#i番目のホテルから2 ** k 日以内に到達可能な
#もっとも右にあるホテル
r = [[-1] * N for k in range(m)]
for i in range(N):
  base = x[i] + L
  p = bisect.bisect_right(x, base)
  #print(p)
  r[0][i] = p - 1

#ダブリング
for k in range(m - 1):
  for i in range(N):
    r[k + 1][i] = r[k][r[k][i]]
#print(r)    
   
def isOK(mid):
  now = a
  pp = int(math.log(mid, 2) + 1)
  for i in range(pp):
    if (mid >> i) & 1:
      now = r[i][now]
      #print(now, a + 1, b + 1, mid)
  if now >= b:
    return True
  else:
    return False
  
Q = int(input())
for i in range(Q):
  a, b = map(int, input().split())
  a, b = a-1, b-1
  if a > b:
    a, b = b, a
  ng = 0
  ok = 2 ** m
  while (abs(ok - ng) > 1):
    mid = int((ok + ng) / 2)
    #print(mid)
    if isOK(mid):
      ok = mid
    else:
      ng = mid
  print(ok)
         

         
         
         