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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:usize,
        a:[i64;n],
    }
    let mut b = a.clone();
    b.sort();
    let mut kohos = vec![];
    kohos.push(b[n / 2]);
    if n / 2 + 1 < n {
        kohos.push(b[n / 2 + 1]);
        kohos.push((b[n / 2] + b[n / 2 + 1]) / 2);
    }
    kohos.push(b[n / 2] + 1);
    kohos.push(b[n / 2] - 1);
    let mut ans = INF;

    for &koho in kohos.iter() {
        let mut lef = koho - (n / 2) as i64;

        let mut ret = 0;
        for i in 0..n {
            ret += (a[i] - lef).abs();
            lef += 1;
        }
        ans = min(ans, ret);
    }
    println!("{}", ans);
}
const INF: i64 = 1 << 60;