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.
-----Partial Score-----
 - 200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.
-----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.
-----Sample Input-----
9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5
-----Sample Output-----
4
2
1
2
For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:
 - Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.
 - Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.
 - Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.
 - Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.
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)
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)