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)

(defun sad-diff (N newlst)
  (- (* 2 (count-if #'minusp newlst)) N))

(defun range (m n &optional l)
  (if (< n m) l
    (range m (1- n) (cons n l)) ))

(defun solve (N lst)
  (setf lst (mapcar #'- lst (range 1 N)))
  (let ((m (reduce #'min lst))
        (n (reduce #'max lst)))
       (do* ((b m (1+ b))
             (l (mapcar (lambda (x) (- x b)) lst)
                (mapcar #'1- lst))
             (sad (reduce 
                   (lambda (x y) (+ x (abs y)))
                   l :initial-value 0 )
                  (+ sad (sad-diff N l)))
             (minsad sad (min sad minsad)))
         ((> b n) minsad) )))

(defvar N (read))
(princ (solve N (loop :repeat N :collect (read))))