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
N = int(input())
X = list(map(int, input().split()))
L = int(input())
from bisect import *
def get_move(X,L,left=False):
  res = [0]*N
  for i in range(N):
    if left:
      res[i] = bisect_left(X,X[i]-L)
    else:
      res[i] = bisect_right(X,X[i]+L)-1
  K = N.bit_length()
  db = [[0]*N for _ in range(K)]
  db[0] = res
  for i in range(1,K):
    for j in range(N):
      db[i][j] = db[i-1][db[i-1][j]]
  return db

def search(dbr,dbl,a,b):
  if a>b:
    db = dbl
    left = True
  else:
    db = dbr
    left = False
  K = N.bit_length()
  ans = 0
  for p in range(K-1,-1,-1):
    if left:
      if b < db[p][a]:
        a = db[p][a]
        ans += 1<<p
    else:
      if b > db[p][a]:
        a = db[p][a]
        ans += 1<<p
  ans += 1
  return ans

dbr = get_move(X,L)
dbl = get_move(X,L,left=True)
Q = int(input())
ans = [0]*Q
for i in range(Q):
  a,b = map(int, input().split())
  ans[i] = search(dbr,dbl,a-1,b-1)
print(*ans, sep='\n')
