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)]
backdoubling=[[-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]]

for i in range(N):
    npos=x[i]-L
    index=bisect.bisect_left(x,npos)
    backdoubling[0][i]=index

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

def forward(num,start):
    for i in range(20):
        if num>>i &1==1:
            start=doubling[i][start]
    return start

def back(num,start):
    for i in range(20):
        if num>>i &1==1:
            start=backdoubling[i][start]
    return start


for _ in range(int(input())):
    a,b=map(int,input().split())
    a-=1;b-=1
    if b>=a:
        s=0
        e=N
        while e-s>1:
            test=(e+s)//2
            if forward(test,a)>=b:
                e=test
            else:
                s=test
        if forward(s,a)>=b:
            print(s)
        else:
            print(e)
    else:
        s=0
        e=N
        while e-s>1:
            test=(e+s)//2
            if b>=back(test,a):
                e=test
            else:
                s=test
        if b>=back(s,a):
            print(s)
        else:
            print(e)