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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(unused_macros)]
use itertools::Itertools;
use std::cmp::{max, min};
use std::collections::*;
use std::fmt::Write as _Write;
use std::i64;
use std::io::{stdin, BufWriter, Read, Write};
use std::usize;

#[allow(unused_macros)]
macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, $var:ident $($r:tt)*) => {
        let $var = parse_val!($it, usize);
        parse!($it $($r)*);
    };
}

#[allow(unused_macros)]
macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: tt),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, u1) => {
        $it.next().unwrap().parse::<usize>().unwrap() -1
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

pub fn msb(mut n: usize) -> usize {
    let mut ret = 0;
    while n > 1 {
        n >>= 1;
        ret += 1;
    }
    ret
}
use std::ops::{Add, Div};
pub fn binary_search<T: Add<Output = T> + Div<Output = T> + PartialEq + From<u8> + Copy>(
    l: T,
    r: T,
    pred: impl Fn(T) -> bool,
) -> T {
    let mut l = l;
    let mut r = r;
    let two = T::from(2_u8);
    loop {
        let m = (l + r) / two;
        if l == m || r == m {
            break l;
        }
        if pred(m) {
            l = m;
        } else {
            r = m;
        }
    }
}

pub fn upper_bound<T: PartialOrd>(v: &[T], val: &T) -> usize {
    (binary_search(-1, v.len() as i64, |i: i64| v[i as usize] <= *val) + 1) as usize
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, n: usize, x: [usize; n], l: usize, q: usize);
    let x: Vec<usize> = x;
    let d = msb(n - 1) + 1;
    let mut tbl: Vec<Vec<usize>> = vec![vec![n; n]; d];
    for (i, xi) in x.iter().enumerate() {
        let mut j = upper_bound(&x, &(xi + l)) - 1;
        if j == n - 1 {
            j = n;
        }
        tbl[0][i] = j;
    }
    for i in 1..d {
        for j in 0..n {
            let k = tbl[i - 1][j];
            if k < n {
                tbl[i][j] = tbl[i - 1][k];
            }
        }
    }
    for _ in 0..q {
        parse!(it, a: u1, b: u1);
        let (mut a, b) = if a > b { (b, a) } else { (a, b) };
        let mut ret = 0;
        while a < b {
            for j in (0..d).rev() {
                if tbl[j][a] <= b || j == 0 {
                    a = tbl[j][a];
                    ret += 1 << j;
                    break;
                }
            }
        }
        println!("{}", ret);
    }
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}
trait ChMinMax {
    fn chmin(&mut self, other: Self);
    fn chmax(&mut self, other: Self);
}
impl<T> ChMinMax for T
where
    T: PartialOrd,
{
    fn chmin(&mut self, other: Self) {
        if *self > other {
            *self = other
        }
    }
    fn chmax(&mut self, other: Self) {
        if *self < other {
            *self = other
        }
    }
}