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)


fn main(){
	let mut s = String::new();
	std::io::stdin().read_line(&mut s).unwrap();
	let n: usize = s.trim().parse().unwrap();
	let mut s = String::new();
	std::io::stdin().read_line(&mut s).unwrap();
	let vec: Vec<&str> = s.trim().split(' ').collect();
	let mut x = 10000;
	for b in 0..30 {
		let mut wx = 0;
		for i in 0..n {
			let vn: i32 = vec[i].parse().unwrap();
			wx += abs(vn - (b + (i + 1) as i32));
		}
		if wx < x {
			x = wx;
		}
	}
	println!("{}", x);
}

fn abs(n: i32) -> i32 {
	if n < 0 {
		n * - 1
	} else {
		n
	}
}