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,bisect

input=sys.stdin.readline

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

doubling=[[-1 for i in range(N)] for j in range(20)]

for i in range(N):
    npos=x[i]+L
    index=bisect.bisect_right(x,npos)
    doubling[0][i]=index-1

for i in range(1,20):
    for j in range(N):
        doubling[i][j]=doubling[i-1][doubling[i-1][j]]

forward=[[-1 for i in range(N)] for j in range(20)]

for i in range(N):
    forward[0][i]=i

for i in range(1,20):
    for j in range(N):
        forward[i][j]=doubling[i-1][forward[i-1][j]]

for _ in range(int(input())):
    a,b=map(int,input().split())
    a-=1;b-=1
    if a>b:
        a,b=b,a
    res=0
    for i in range(19,-1,-1):
        if b>forward[i][a]:
            a=doubling[i][a]
            res+=2**i
    print(res)