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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)] use proconio::{input, marker::{Bytes, Chars, Usize1, Isize1}};
#[allow(unused_imports)] use std::cmp::{min, max};
#[allow(unused_imports)] use superslice::Ext as _;

#[proconio::fastout]
fn main() {
	input! {
		n: usize,
		a: [isize; n],
	}

	// x=ai-i とおく
	// bを自由に決め、abs(x-b)の総和を最小化する
	// bをxの中央値にすればよい

	let mut x = vec![0isize; n];
	for i in 0..n {
		x[i] = a[i] - i as isize -1;
	}
	x.sort();
	let b;
	if x.len() % 2 == 1 {
		b = x[x.len()/2];
	}
	else {
		b = (x[x.len()/2-1] + x[x.len()/2]) / 2;
	}

	let mut ans = 0isize;
	for i in 0..n {
		ans += (a[i]-(b+i as isize+1)).abs();
	}

	println!("{}", ans);
}