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 (1.15.1) (judge verdict: Time Limit Exceeded)

use std::cmp;

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let x: Vec<u64> = sc.vec(n);

    let mut y = vec![vec![0; n]; 30];
    for i in 0..(n - 1) {
        y[0][i] = x[i + 1] - x[i];
    }
    for t in 0..(y.len() - 1) {
        for i in 0..n {
            let next_pos = i + (1 << t);
            if next_pos >= n {
                break;
            }
            if y[t][i] == 0 || y[t][next_pos] == 0 {
                continue;
            }
            y[t + 1][i] = y[t][i] + y[t][next_pos];
        }
    }

    let l: u64 = sc.read();
    let mut go = vec![vec![0; n]; 5];
    for i in 0..n {
        let mut cur = i;
        let mut t = y.len() - 1;
        let mut l = l;
        loop {
            if y[t][cur] == 0 || y[t][cur] > l {
                if t > 0 {
                    t -= 1;
                } else {
                    break;
                }
            } else {
                l -= y[t][cur];
                cur += 1 << t;
            }
        }
        go[0][i] = cur;
    }

    for t in 1..go.len() {
        for i in 0..n {
            go[t][i] = go[t - 1][go[t - 1][i]];
        }
    }

    let q: usize = sc.read();
    for _ in 0..q {
        let a: usize = sc.read::<usize>() - 1;
        let b: usize = sc.read::<usize>() - 1;

        let (mut a, b) = (cmp::min(a, b), cmp::max(a, b));
        let mut ans = 0;
        for i in (0..go.len()).rev() {
            while go[i][a] <= b {
                ans += 1 << i;
                a = go[i][a];
            }
            if i == 0 && a < b {
                assert!(go[i][a] >= b);
                ans += 1;
            }
        }
        println!("{}", ans);
    }
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}