Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused)]

use std::{cell, cmp, collections, fmt, io, iter, ops, str};

use cell::{Cell, RefCell};
use cmp::Ordering::{Equal, Greater, Less};
use collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};
use io::{Read, Write};

#[cfg(feature = "debug")]
macro_rules! debug {
    ($($args: tt)*) => { eprint!($($args)*) };
}

#[cfg(feature = "debug")]
macro_rules! debugln {
    ($($args: tt)*) => { eprintln!($($args)*) };
}

#[cfg(not(feature = "debug"))]
macro_rules! debug {
    ($($args:tt)*) => {};
}

#[cfg(not(feature = "debug"))]
macro_rules! debugln {
    ($($args:tt)*) => {};
}

macro_rules! vmax {
    ($x: expr, $y: expr) => { cmp::max($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::max($x, vmax!($($args),*)) };
}

macro_rules! vmin {
    ($x: expr, $y: expr) => { cmp::min($x, $y) };
    ($x: expr, $($args: expr),*) => { cmp::min($x, vmin!($($args),*)) };
}

fn main() {
    let n = parse_line::<usize>();
    let a = parse_vec::<i32>();

    let (mut left, mut right): (i32, i32) = (
        *a.iter().min().unwrap() - n as i32,
        *a.iter().max().unwrap() + n as i32,
    );

    loop {
        let l = (left * 2 + right) / 3;
        let r = (left + right * 2) / 3;

        if sadness(&a, l) < sadness(&a, r) {
            if right == r {
                break;
            }

            right = r;
        } else {
            if left == l {
                break;
            }

            left = l;
        }
    }

    debugln!(
        "{} {}, {} {}",
        left,
        sadness(&a, left),
        right,
        sadness(&a, right)
    );

    let ans = vmin!(
        sadness(&a, left),
        sadness(&a, (left + right) / 2),
        sadness(&a, right)
    );

    println!("{}", ans);
}

fn sadness(a: &[i32], b: i32) -> i32 {
    a.iter()
        .enumerate()
        .map(|(i, a)| (a - (b + (i + 1) as i32)).abs())
        .sum()
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test() {
        //
    }
}

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_owned()
}

fn read_word() -> String {
    const CAPACITY: usize = 16;

    let mut stdin = io::stdin();
    let mut byte: [u8; 1] = [0];

    loop {
        let mut buf = Vec::with_capacity(CAPACITY);

        loop {
            let res = stdin.read(&mut byte);

            if res.unwrap_or(0) == 0 || byte[0] <= b' ' {
                break;
            } else {
                buf.push(byte[0]);
            }
        }

        if !buf.is_empty() {
            return String::from_utf8(buf).unwrap();
        }
    }
}

fn parse_line<T: str::FromStr>() -> T {
    read_line().parse().ok().unwrap()
}

fn parse_word<T: str::FromStr>() -> T {
    read_word().parse().ok().unwrap()
}

fn parse_vec<T: str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn flush() {
    io::stdout().flush();
}

fn next_prime(x: i32) -> i32 {
    for i in (x + 1).. {
        if is_prime(i) {
            return i;
        }
    }

    panic!("attempt to add with overflow");
}

fn is_prime(x: i32) -> bool {
    let ceil = f64::from(x).sqrt().ceil() as i32;
    x == 2 || (2..(ceil + 1)).all(|i| x % i != 0)
}