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 = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
x = list(map(int, input().split()))
l = int(input())
q = int(input())
ps = [None]*n
# ps2 = [None]*n
j = 0
for i in range(n):
    if j<i:
        j = i
    while j+1<n and x[j+1]-x[i]<=l:
        j += 1
    ps[i] = j
# ダブリング
def double(ps):
    # global: n=psのサイズ
    k = 0
    n = len(ps)
    while pow(2,k)<n:
        k += 1
    prev = [[None]*n for _ in range(k)] # ノードjから2^i個上の上司
    for j in range(n):
        prev[0][j] = ps[j]
    for i in range(1,k):
        for j in range(n):
            p = prev[i-1][j]
            if p>=0:
                prev[i][j] = prev[i-1][p]
            else:
                prev[i][j] = p
    return prev
dl = double(ps)
ans = [None]*q
for i in range(q):
    a,b = map(lambda x: int(x)-1, input().split())
    a,b = min(a,b), max(a,b)
#     print(a,b)
    res = 0
    tmp = float("inf")
    for k in range(len(dl)-1, -1, -1):
        if dl[k][a]<b:
            a = dl[k][a]
            res += pow(2,k)
#         elif dl[k][a]==b:
#             tmp = res+pow(2,k)
#             break
        else:
            tmp = min(tmp, res+pow(2,k))
    ans[i] = tmp
write("\n".join(map(str, ans)))