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)

#![allow(unused_imports)]
#![allow(dead_code)]
#![allow(unused_must_use)]
use std::io::{stdin, stdout, stderr, Write, BufWriter, BufReader, BufRead};

macro_rules! read_from_line {
    ($inbuf:ident => $($name:ident : $ty:ty),* ) => {
        let mut buf = String::new();
        $inbuf.read_line(&mut buf).unwrap();
        buf.pop();
        let mut words = buf.split_whitespace();
        $(
            let $name:$ty = words.next().unwrap().parse().unwrap();
        )*
    };
}

macro_rules! read_many {
    ($inbuf:ident => $name:ident : $ty:ty) => {
        let $name: Vec<$ty> = strio::read_many_from_line(&mut $inbuf);
    };
}

fn main() {
    let cout = stdout();
    let mut cout = BufWriter::new(cout.lock());
    let cin = stdin();
    let mut cin = BufReader::new(cin.lock());

    //read_from_line!(cin => a:i32, b:String);
    //let xs: Vec<i32> = strio::read_many_from_line(&mut cin);
    
    read_from_line!(cin => _n:i32);
    read_many!(cin => xs:i64);
    let mut xs_sorted = xs.iter().enumerate().map(|(ix, x)| x - (ix as i64)).collect::<Vec<i64>>();
    xs_sorted.sort();
    let mut mids = vec![];
    if xs_sorted.len() % 2 == 0 {
        mids.push(xs_sorted.len() / 2);
        mids.push(xs_sorted.len() / 2 - 1);
    } else {
        mids.push(xs_sorted.len() / 2);
    }

    let ans: i64 = mids.iter().map(|mid| {
        let midv = xs_sorted[*mid];
        xs_sorted.iter().map(|x| (x - midv).abs()).sum()
    }).min().unwrap();

    writeln!(cout, "{}", ans);
}

mod strio {
    use std::str::FromStr;
    use std;

    pub fn read_from_line<T, R> (r: &mut R) -> T where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.parse().unwrap()
    }

    pub fn read_many_from_line<T, R> (r: &mut R) -> Vec<T> where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.split_whitespace().map(|x| x.parse().unwrap()).collect()
    }
}