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

def wantp(p,day):

    for i in range(len(db)):
        i = len(db)-1-i

        if day & (2 ** i) > 0:
            p = db[i][p]

        #print (day,i)

    return p


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

able = []

for i in range(N):

    able.append(bisect.bisect_right(x,x[i] + L) - 1)


db = [able]

while min(db[-1]) != N-1:

    new = []

    for i in range(N):

        new.append(db[-1][db[-1][i]])

    db.append(new)


Q = int(input())

for loop in range(Q):

    a,b = map(int,input().split())
    if a > b:
        t = a
        a = b
        b = t
    a -= 1
    b -= 1

    l = 0
    r = 2 ** len(db)

    while r-l != 1:

        m = (l+r) // 2

        np = wantp(a,m)
        #print (a,m,np)

        if np < b:
            l = m
        else:
            r = m

    print (r)
