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 sys
input = sys.stdin.readline
import bisect

def main():
  n = int(input())
  X = list(map(int, input().split()))
  l = int(input())
  U = 17
  dp = [[0]*n for _ in range(U+1)]
  for i, x in enumerate(X):
    t = bisect.bisect_left(X, x+l)
    dp[0][i] = bisect.bisect_right(X, x+l) - 1
  for k in range(U):
    for i in range(n):
      dp[k+1][i] = dp[k][dp[k][i]]
  q = int(input())
  for _ in range(q):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    if a > b:
      a, b = b, a
    res = 1
    for k in range(U, -1, -1):
      if dp[k][a] < b:
        a = dp[k][a]
        res += (1<<k)
    print(res)
if __name__ == "__main__":
  main()