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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defvar *n* (read))

(defun split-string (str)
  (let ((string-position (position #\Space str)))
    (cond
      ((null string-position) (list str))
      (t (cons (subseq str 0 string-position) (split-string (subseq str (1+ string-position))))))))
 
(defun LinearApproximation ()
  (let ((B) (sb 0) (count 0))
    (dotimes (i *n*)
      (push  (- (read) (1+ i)) B))
    (sort B #'<)
    (if (evenp *n*)
        (setf sb (floor (+ (nth (floor (length B) 2) B)
                              (nth (1+ (floor (length B) 2)) B)) 2)) 
        (setf sb  (nth (floor (length B) 2) B)))
    (apply #'+ (mapcar (lambda (Bi)
               (abs (- Bi sb))) B))))
 
(format t "~A~%" (LinearApproximation))