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: Wrong Answer)

#[allow(unused_macros)]
macro_rules! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            line.pop();
            line
        }
    )
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let iter = line.split_whitespace();
            iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    )
}

fn solve(mut aa: Vec<i64>) -> i64 {
    use std::cmp::min;

    let n = aa.len();

    for i in 0..n {
        aa[i] -= (i+1) as i64;
    }

    let mut s = 0;
    for &a in aa.iter() {
        s += a as i64;
    }

    let avg = s / n as i64;

    let mut ret1 = 0;
    let mut ret2 = 0;
    let mut ret3 = 0;

    for &a in aa.iter() {
        ret1 += (a-avg).abs();
    }


    for &a in aa.iter() {
        ret2 += (a-avg-1).abs();
    }


    for &a in aa.iter() {
        ret3 += (a-avg+1).abs();
    }

    min(ret1, min(ret2, ret3))
}


fn main() {
    read_line!();

    let aa = parse_vec!(i64);
    println!("{}", solve(aa));
}

#[test]
fn solve_test() {
    assert_eq!(solve(vec![2,2,3,5,5]), 2);
    assert_eq!(solve(vec![1,2,3,4,5,6,7,8,9]), 0);
    assert_eq!(solve(vec![6,5,4,3,2,1]), 18);
    assert_eq!(solve(vec![1,1,1,1,2,3,4]), 6);
}