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)

use std::io;
use std::cmp;

fn main() {
    let n = read_one::<usize>();
    let mut a = read::<isize>();

    for i in 0..n {
        a[i] -= (i + 1) as isize;
    }

    /* mean
    let d: isize = a.iter().sum();
    let b = d / n as isize;

    let mut ans = 100_000_000_000;
    for j in 0..5 {
        let mut s = 0;
        for k in 0..n {
            s += (a[k] - (b - (j - 2))).abs();
        }
        ans = cmp::min(ans, s);
    }
    println!("{}", ans);
    */

    /* median */
    let median;
    let mut b = a.clone();
    b.sort();
    if n % 2 == 0 {
        median = (b[n / 2] + b[(n - 1)/ 2]) / 2;
    } else {
        median = b[(n - 1) / 2];
    }

    let mut ans = 100_000_000_000;
    for j in 0..5 {
        let mut s = 0;
        for k in 0..n {
            s += (a[k] - (median - (j - 2))).abs();
        }
        ans = cmp::min(ans, s);

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

#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}