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: Accepted)

use std::io::*;
use std::str::*;

fn read_from_stdin<T: FromStr>() -> T {
    let temp = stdin();
    let mut temp = temp.lock();
    read(&mut temp).unwrap()
}

fn read<T: FromStr>(s: &mut StdinLock) -> Option<T> {
    let s = s.by_ref()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn main() {
    let n: usize = read_from_stdin();
    let mut array = Vec::new();
    for i in 1..n + 1 {
        let a: i64 = read_from_stdin();
        array.push(a - i as i64);
    }
    array.sort();

    if n % 2 == 0 {
        let (b_pre, b_suc) = (array[n / 2 - 1], array[n / 2]);
        let res_pre: i64 = array.iter().map(|x| (x - b_pre).abs()).sum::<i64>();
        let res_suc: i64 = array.iter().map(|x| (x - b_suc).abs()).sum::<i64>();
        println!("{}", std::cmp::min(res_pre, res_suc));
    } else {
        let b = array[n / 2];
        let res: i64 = array.iter().map(|x| (x - b).abs()).sum::<i64>();
        println!("{}", res);
    }
}