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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as BS
import Data.Char
import Data.List

main = do
  li <- BS.getLine
  let Just (n,_) = BS.readInt li
  li <- BS.getLine
  let as = unfoldr (BS.readInt . BS.dropWhile isSpace) li
  let ans = compute n as
  print ans

compute :: Int -> [Int] -> Int
compute n as = case signum q of
  0 -> score p as
  s -> min (score p as) (score (p+s) as)
  where
    total = sum as - n * pred n `div` 2
    (p,q) = quotRem total n

score b as = sum $ zipWith f as [b..]
  where
    f a b = abs (a - b)

{-
0 < Ai なので、
b = average $ zipWith (-) as [0..]
とすればよいだけでは。averageが四捨五入するように気を付ける。
b < 0のときのそれが要注意だった。
あれ？
-}