200602: [AtCoder]ARC060 E - Tak and Hotels

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 $10$.