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 OCaml (4.02.3) (judge verdict: Accepted)

let input_int_array n =
	Array.init n (fun _ -> Scanf.scanf "%d " (fun v -> v))
let get_int () = Scanf.scanf "%d " (fun v -> v)

let c a b =
	Array.fold_left (fun u v -> u + abs (v-b)) 0 a

let () =
	let n = get_int ()
	in let a = Array.mapi
		(fun i v -> v - i - 1)
		(input_int_array n)
	in let b =
		let b = Array.copy a
		in Array.sort Pervasives.compare b; b
	in
	(
		if n mod 2 = 1 then (
			c b b.(Array.length b / 2)
		) else (
			min
				(c b b.(Array.length b / 2))
				(c b b.(Array.length b / 2 - 1))
		)
	)
	|> string_of_int |> print_endline