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: Time Limit Exceeded)

fn main() {
    let n: i64 = read();
    let a: Vec<i64> = read_vec();

    let b_min = -200000;
    let b_max = 1000000000;
    let mut r = 10000000000000000;

    let b = (abs_ab(&a, b_min) - abs_ab(&a, b_max)) / 2 / n + (b_max + b_min) / 2;

    for i in 0..2000000 {
        let r1 = abs_ab(&a, b + i);
        if r1 <= r {
            r = r1;
        } else {
            break;
        }
    }
    for i in 0..2000000 {
        let r1 = abs_ab(&a, b - i);
        if r1 <= r {
            r = r1;
        } else {
            break;
        }
    }
    println!("{}", r);
}

fn abs_ab(a: &Vec<i64>, b: i64) -> i64 {
    let mut r = 0;
    for (i, item) in a.iter().enumerate() {
        r += (b + i as i64 - *item).abs();
    }
    r
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}