Problem:
Score : 700 points

Problem Statement

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 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

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.

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

import bisect


n = int(input())
x = list(map(int, input().split()))
l = int(input())
q = int(input())
info = [list(map(int, input().split())) for i in range(q)]


#logテーブルを作成する
log_table = [[0]*n for i in range(17)]
for i in range(n):
    log_table[0][i] = bisect.bisect_right(x, x[i] + l) - 1
for j in range(1, 17):
    for i in range(n):
        log_table[j][i] = log_table[j-1][log_table[j-1][i]]

#二分探索で解を求める
def solve(_from, to, day):
    pos = _from
    i = 0
    while day:
        if day // 2 > 0:
            if day % 2 == 1:
                pos = log_table[i][pos]
            i += 1
            day = day // 2
        else:
            if day % 2 == 1:
                pos = log_table[i][pos]
            break
    if to <= pos:
        return True
    else:
        return False

#クエリに答える
for i in range(q):
    ok = n - 1
    ng = 0
    start, goal = info[i]
    start -= 1
    goal -= 1
    if start > goal:
        start, goal = goal, start
    while abs(ok - ng) > 1:
        mid = (ok + ng) // 2
        if solve(start, goal, mid):
            ok = mid
        else:
            ng = mid
    print(ok)