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)

use proconio::input;

fn main() {
    input! {
        n: usize,
        mut aa: [isize; n],
    }

    for (i, a) in aa.iter_mut().enumerate() {
        *a -= i as isize + 1;
    }

    let sum = aa.iter().copied().sum::<isize>();
    let val = sum / aa.len() as isize;

    let ans1 = aa.iter().copied().map(|a| (a - val).abs()).sum::<isize>();
    let ans2 = aa.iter().copied().map(|a| (a - val - 1).abs()).sum::<isize>();
    let ans3 = aa.iter().copied().map(|a| (a - val + 1).abs()).sum::<isize>();

    let ans = std::cmp::min(ans1, ans2);
    let ans = std::cmp::min(ans, ans3);

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