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::str::FromStr;
use std::fmt::Debug;
use std::io::stdin as S;

fn read_input<T>() -> Vec<T>
where T: FromStr,<T as FromStr>::Err: Debug {
    let mut input = String::new();
    S().read_line(&mut input).unwrap();
    input.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()
}

fn main(){
    let n: Vec<i32> = read_input();
    let n = n[0];
    let mut a: Vec<i64> = read_input();

    for (i,x) in a.iter_mut().enumerate(){
        *x -= i as i64 + 1;
    }
    a.sort();

    let b = a[(n as usize/2)];

    let ans: i64 = a.iter().fold(0,|sum,x| sum + (x-b).abs());
    println!("{}",ans);
}