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)

// input! macro is published in the following URLs.
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
// https://github.com/tanakh/competitive-rs.git
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    input! {
        n: usize,
        a_s: [i64; n],
    }
    // (2 - (b + 1)).abs() + (2 - (b + 2)).abs() + (3 - (b + 3)).abs() + (5 - (b + 4)).abs() + (5 - (b + 5)).abs()
    // (2 - (b + 1)).abs(): -2 => 3, -1 => 2, 0 => 1, 1 => 0, 2 => 1   min: a - i = 1
    // (2 - (b + 2)).abs(): -2 => 2, -1 => 1, 0 => 0, 1 => 1, 2 => 2   min: a - i = 0
    // (3 - (b + 3)).abs(): -2 => 2, -1 => 1, 0 => 0, 1 => 1, 2 => 2   min: a - i = 0
    // (5 - (b + 4)).abs(): -2 => 3, -1 => 2, 0 => 1, 1 => 0, 2 => 1   min: a - i = 1
    // (5 - (b + 5)).abs(): -2 => 2, -1 => 1, 0 => 0, 1 => 1, 2 => 2   min: a - i = 0
    let mut mins = a_s
        .iter()
        .enumerate()
        .map(|(i, a)| a - (i as i64 + 1))
        .collect::<Vec<_>>();
    mins.sort();
    let mid = mins[n / 2];
    let bs = [mid.saturating_sub(1), mid, mid + 1];
    let ans = bs
        .iter()
        .map(|b| {
            a_s.iter()
                .enumerate()
                .map(|(i, a)| (a - (b + i as i64 + 1)).abs())
                .sum::<i64>()
        })
        .min()
        .unwrap();
    println!("{}", ans);
}