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

n=int(raw_input())
x=map(int,raw_input().split())+[float('inf')]
l=int(raw_input())
q=int(raw_input())
r=[[0]*20 for _ in xrange(n)]

for i in xrange(n):
    if x[i]+l==x[bisect.bisect_left(x,x[i]+l)]:
        r[i][0]=bisect.bisect_left(x,x[i]+l)
    else:
        r[i][0]=bisect.bisect_left(x,x[i]+l)-1

for k in xrange(19):
    for i in xrange(n):
        r[i][k+1]=r[r[i][k]][k]
        
for i in xrange(q):
    a,b=map(int,raw_input().split())
    a-=1
    b-=1
    ans=0
    if a>b:
        a,b=b,a
    while 1:
        if bisect.bisect_left(r[a],b)>=1:
            ans+=1<<(bisect.bisect_left(r[a],b)-1)
            a=r[a][bisect.bisect_left(r[a],b)-1]
        else :
            ans+=1<<bisect.bisect_left(r[a],b)
            break
    print(ans)