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: Runtime Error)

fn main() {
    // stdinのロックを取得し、StdinReaderを作る。
    let stdin = std::io::stdin();
    let mut r = utils::StdinReader::new(stdin.lock());

    let count = r.readl::<i32>();  // 次の改行まで読む

    let mut xs: Vec<i32> = Vec::new();
    for i in 1i32..count {
        xs.push(r.reads::<i32>() - i);
    }
    xs.push(r.readl::<i32>() - count);

    xs.sort();
    let m =  xs.iter().nth((count  / 2) as usize + 1).unwrap();
    println!("{}",  xs.iter().fold(0i32, |acc, b| acc + b - m));
}

mod utils {

    use std::io::BufRead;
    use std::str::{self, FromStr};

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(reader: R) -> StdinReader<R> {
            StdinReader {
                reader: reader,
                buf: Vec::new(),
            }
        }

        // 区切り文字：スペース
        pub fn reads<T: FromStr>(&mut self) -> T {
            self.read_until(b' ')
        }

        // 区切り文字：改行
        pub fn readl<T: FromStr>(&mut self) -> T {
            self.read_until(b'\n')
        }

        pub fn read_until<T: FromStr>(&mut self, delim: u8) -> T {
            // self.bufに次のトークンをセットする
            loop {
                self.buf.clear();
                let len = self.reader
                    .read_until(delim, &mut self.buf)
                    .expect("failed reading bytes");
                match len {
                    0 => panic!("early eof"),
                    1 if self.buf[0] == delim => (), // 区切り文字だけなのでもう一度ループ
                    _ => {
                        // トークンが得られた
                        // 最後の文字が区切り文字なら削除
                        if self.buf[len - 1] == delim {
                            self.buf.truncate(len - 1);
                        }
                        break; // ループから脱出
                    }
                }
            }

            // 文字列をT型へパースする
            let elem = str::from_utf8(&self.buf).expect("invalid utf-8 string");
            elem.parse().unwrap_or_else(|_| panic!(format!("failed parsing: {}", elem)))
        }
    }

}