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: Time Limit Exceeded)

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 test a b =
  Array.fold_left (fun (u,i) v -> 
    (* Printf.printf "  %d::abs(%d-(%d+%d))=%d\n"
      i v b i (abs (v-(b+i)))
    ; *)
    (u + (abs (v - (b+i)))), i+1) (0,1) a
  |> fst

let () =
  let n = get_int ()
  in let a = input_int_array n
  in let l = a |> Array.to_list
  in let lmax = List.fold_left max min_int l
  in let v = ref lmax in let f = ref true
  in let la = ref max_int
  in while !f do
    let r = test a !v
    in
    (* Printf.printf "%d::%d\n" !v r; *)
    if r < !la then (
      la := r; v := !v - 1
    ) else (
      f := false
    )
  done;
  !la |> string_of_int |> print_endline