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: Accepted)

(defun moge ()
  (let ((n (read))
        (lst nil))
    (dotimes (i n)
      (push (read) lst))
    (reverse lst)))


(defun chuou (b-lst)
  (let* ((len (length b-lst))
         (chuou-n (floor len 2))
         (new-lst (sort b-lst #'<)))
    (if (oddp len)
        (nth chuou-n new-lst)
        (let ((c1 (nth chuou-n new-lst))
              (c2 (nth (1- chuou-n) new-lst)))
          (floor (+ c1 c2) 2)))))

(defun hoge ()
  (let* ((lst (moge))
         (b-lst (loop :for a :in lst
                      :for i :from 1
                      :collect (- a i)))
         (b (chuou b-lst))
         (v (loop :for a :in lst
                  :for i :from 1
                  :sum (abs (- a (+ b i))))))
    (format t "~D~%" v)))


(hoge)